numbers
Numbers are like words for counting! We use them for many things.
You use numbers to say how many apples you have, like one, two, or three.
They also tell us how old we are, or what page we are on in a book.
So, numbers help us count and know quantities.
Numbers are like special words or signs that help us count things. For example, when you count your fingers, you use numbers like one, two, three.
We also use numbers to tell how many of something there are, like "I have two apples."
They can also help us know where something is in a list, like "This is the first toy."
So, numbers are very important for counting, knowing amounts, and ordering things.
Numbers are fundamental to mathematics and daily life, serving as symbols or words that express a mathematical value. They are used extensively for various purposes, such as counting objects, measuring quantities, or labeling items. For instance, you might use numbers to count how many apples are in a basket, to measure the length of a room, or to label pages in a book.
Beyond just representing a specific quantity, numbers can also denote a position within a sequence. Think of house numbers on a street or the order of runners in a race – these all use numbers to establish a clear sequence or rank. Understanding numbers is crucial for navigating everything from basic arithmetic to complex data analysis.
§ What does it mean?
The word "numbers" refers to symbols or words that represent a mathematical value. These values are fundamental to how we quantify and organize the world around us. Think of them as the building blocks of mathematics.
- DEFINITION
- Symbols or words representing a mathematical value used for counting, measuring, or labeling. They can indicate a specific quantity or a position in a sequence.
Essentially, numbers are abstract concepts that we use to describe 'how many' of something there are, or 'where' something is in an ordered list. For example, when you say you have "two apples," the word "two" is a number representing a quantity. When you say you are on "page five" of a book, "five" is a number indicating a position in a sequence.
§ When do people use "numbers"?
People use numbers in virtually every aspect of daily life, often without even realizing it. Their applications are incredibly broad and span across various fields and situations.
§ Counting and Quantifying
One of the most common uses of numbers is for counting. From simple tasks like counting money to more complex ones like tracking populations, numbers help us understand quantities.
Can you tell me how many numbers of eggs we have left in the fridge?
This sentence uses "numbers" in a way that implies asking for a quantity, specifically the count of eggs.
§ Measuring
Measurement relies heavily on numbers. Whether it's measuring length, weight, temperature, or time, numbers provide the values that define these measurements.
The thermometer showed high numbers, indicating a fever.
Here, "high numbers" refers to the numerical values on the thermometer scale, used to measure temperature.
§ Labeling and Identification
Numbers are also used as labels for identification. This includes phone numbers, house numbers, product serial numbers, and so on. They help us uniquely identify individual items or entities.
Could you please write down your contact numbers for me?
In this instance, "contact numbers" refers to phone numbers used for communication.
§ Ordering and Sequencing
When we talk about a position in a sequence, numbers are indispensable. This includes things like page numbers in a book, street numbers on a street, or the order of items in a list.
Please remember the lottery numbers for tonight's drawing.
Here, "lottery numbers" are a specific set of digits that have a sequential or unique identification purpose.
§ Mathematical Operations
Of course, numbers are the core of all mathematical operations – addition, subtraction, multiplication, and division. They allow us to perform calculations and solve problems.
Understanding numbers is crucial for basic literacy and for navigating the modern world. They are more than just symbols; they are a universal language that helps us understand, communicate, and interact with our environment.
Financial Transactions: Whether it's budgeting, banking, or shopping, numbers are central to managing money.
Science and Technology: All scientific research, engineering, and technological advancements rely heavily on numbers for data analysis, modeling, and calculation.
Sports: Scores, statistics, and player identifications all involve numbers.
Dates and Times: We use numbers to mark days, months, years, hours, and minutes.
In summary, numbers are an integral part of human communication and understanding. They provide a framework for organizing information, quantifying the world, and performing essential tasks in almost every aspect of our lives.
§ Similar words and when to use this one vs alternatives
- DEFINITION
- Symbols or words representing a mathematical value used for counting, measuring, or labeling. They can indicate a specific quantity or a position in a sequence.
The numbers on the clock indicated it was almost midnight.
Digits: This refers to the individual symbols (0, 1, 2, 3, 4, 5, 6, 7, 8, 9) that make up a number. For example, the number 345 has three digits. You would use 'digits' when talking about the individual components of a number, rather than the value itself. Please enter the four digits of your PIN.
Figures: This word can be used interchangeably with 'numbers' in some contexts, especially when referring to statistical data or numerical representations. However, 'figures' can also refer to shapes or diagrams, so context is important. When discussing financial data or statistics, 'figures' is a common and appropriate alternative. The sales figures for this quarter are impressive.
Quantities: This term specifically refers to an amount or number of something. While 'numbers' can describe a quantity, 'quantities' focuses on the measurable aspect. If you are talking about the measurable extent of something, 'quantities' is more precise. We need to order larger quantities of raw materials.
Amounts: Similar to 'quantities,' 'amounts' refers to the total or sum of something, often uncountable things. While 'numbers' can apply to both countable and uncountable things, 'amounts' is typically used for things that cannot be individually counted (e.g., amount of water, amount of money). A significant amount of effort was put into the project.
Statistics: This term refers to numerical facts or data, especially those collected, analyzed, and interpreted systematically. 'Numbers' can be part of statistics, but 'statistics' implies a broader field of study or a collection of analyzed data. Use 'statistics' when referring to numerical information that has been gathered and processed to understand a phenomenon. The government released new statistics on unemployment.
How Formal Is It?
"Please ensure all financial documents contain accurate numerals for auditing purposes."
"The survey results showed that a significant number of people preferred the new product."
"Can you quickly run through the figures for the sales report before the meeting?"
"Let's learn our counts from one to ten today!"
"I need your digits so I can text you about the party later."
Exemples par niveau
I can count to ten. These are small numbers.
Я могу посчитать до десяти. Это маленькие числа.
Here 'numbers' refers to the mathematical values used in counting.
What are your favorite numbers?
Какие твои любимые числа?
In this sentence, 'numbers' is used to ask about preferred mathematical symbols.
There are many numbers on the clock.
На часах много цифр.
'Numbers' refers to the digits on the clock face.
Can you write the numbers one to five?
Можешь написать числа от одного до пяти?
Here 'numbers' means the written symbols for counting.
My phone number has ten numbers.
Мой номер телефона состоит из десяти цифр.
'Numbers' refers to the digits that make up a phone number.
Look at the numbers on this page.
Посмотри на цифры на этой странице.
'Numbers' refers to the numerical figures printed on the page.
We learned about big numbers today.
Сегодня мы узнали о больших числах.
Here, 'numbers' refers to mathematical values that are large in quantity.
How many numbers are in your age?
Сколько цифр в твоем возрасте?
'Numbers' here refers to the digits used to express an age.
I can count to ten using numbers.
Puedo contar hasta diez usando números.
What are your favorite numbers?
¿Cuáles son tus números favoritos?
She wrote the numbers from one to five.
Ella escribió los números del uno al cinco.
There are many numbers on the clock.
Hay muchos números en el reloj.
Can you tell me the phone numbers of your friends?
¿Puedes decirme los números de teléfono de tus amigos?
The bus has numbers on the front.
El autobús tiene números en la parte delantera.
We learned about big numbers in school today.
Aprendimos sobre números grandes en la escuela hoy.
Please write the numbers clearly so I can read them.
Por favor, escribe los números claramente para que pueda leerlos.
The phone number has ten digits.
전화번호는 열 자리 숫자입니다.
Can you write the numbers from one to ten?
1부터 10까지 숫자를 쓸 수 있나요?
She loves playing with numbers and solving math problems.
그녀는 숫자 가지고 놀고 수학 문제 푸는 것을 좋아해요.
The small numbers on the clock are hard to see.
시계의 작은 숫자들은 보기 어렵다.
We need to check these numbers carefully before submitting the report.
보고서를 제출하기 전에 이 숫자들을 신중하게 확인해야 합니다.
The winning lottery numbers were announced last night.
당첨된 복권 번호가 어젯밤에 발표되었습니다.
There are many numbers on this page; it's a financial document.
이 페이지에는 많은 숫자가 있습니다. 재무 문서입니다.
The scientist collected data and analyzed the numbers.
과학자는 데이터를 수집하고 숫자를 분석했습니다.
The census collected data on the number of residents in each household.
The census collected data on the *count* of residents in each household.
Here, 'number' refers to a specific quantity.
She has my phone number, but she hasn't called yet.
She has my phone *digits*, but she hasn't called yet.
'Phone number' is a common collocation referring to a sequence of digits used for communication.
Can you please write down these numbers for me, so I don't forget them?
Can you please write down these *numerical figures* for me, so I don't forget them?
This sentence uses 'numbers' in a general sense, referring to digits.
The recent report showed a significant increase in the number of people working from home.
The recent report showed a significant increase in the *quantity* of people working from home.
'The number of' is often used to refer to a quantifiable amount of something.
He's very good with numbers and can do complex calculations in his head.
He's very good with *mathematics* and can do complex calculations in his head.
In this context, 'numbers' refers to arithmetic and mathematical concepts.
The page numbers were missing, making it difficult to find specific information.
The page *indices* were missing, making it difficult to find specific information.
'Page numbers' refers to the numerical labels given to individual pages in a document.
We need to analyze these statistics and interpret what the numbers are telling us.
We need to analyze these statistics and interpret what the *data* are telling us.
Here, 'numbers' is used informally to mean data or statistics.
The winning lottery numbers were announced on the evening news.
The winning lottery *digits* were announced on the evening news.
'Lottery numbers' refers to the specific sequence of digits chosen in a lottery.
The government released the latest economic numbers, showing a slight increase in inflation.
The government released the latest economic figures, showing a slight increase in inflation.
Here, 'numbers' refers to statistical data or figures.
She has a real knack for crunching numbers and can quickly analyze complex financial reports.
She has a real knack for calculating figures and can quickly analyze complex financial reports.
'Crunching numbers' is an idiom meaning to perform calculations or analyze data.
The survey results indicate that a significant number of people are concerned about climate change.
The survey results indicate that a large number of people are concerned about climate change.
'A significant number of' is a common phrase to indicate a large quantity.
Despite the challenges, the team managed to put up some impressive numbers in terms of sales this quarter.
Despite the challenges, the team managed to achieve some impressive figures in terms of sales this quarter.
'Put up numbers' is an informal expression meaning to achieve or produce certain results, often in sports or business.
The scientist spent years poring over the numbers, trying to find a pattern in the experimental data.
The scientist spent years meticulously examining the figures, trying to find a pattern in the experimental data.
'Poring over numbers' implies careful and detailed examination of data.
While the exact numbers are still being compiled, early estimates suggest a record turnout for the election.
While the exact figures are still being compiled, early estimates suggest a record turnout for the election.
Here, 'numbers' refers to the precise count or statistics.
The company's performance has been consistently good, with growth in both revenue and customer numbers.
The company's performance has been consistently good, with growth in both revenue and the number of customers.
The plural 'numbers' can refer to the quantity of something, like customers.
He's always been good with numbers, which is why he chose a career in finance.
He's always been good with mathematics, which is why he chose a career in finance.
'Good with numbers' is an idiom meaning to be skilled at mathematics or calculations.
The sheer numbers involved in the global migration crisis present an unprecedented challenge for international cooperation and resource allocation.
The sheer numbers involved: the large quantities/amount involved
Here 'numbers' refers to the quantity of people.
While the qualitative data offered rich insights, the statistical numbers ultimately underpinned the veracity of our research findings.
the statistical numbers: the numerical data
Used here in the sense of 'data' or 'figures'.
Attempts to quantify the intangible benefits of cultural exchange often struggle to assign meaningful numbers to subjective experiences.
assign meaningful numbers: attribute significant numerical values
Used with 'assign' to mean 'to give a numerical value'.
Despite the prevailing optimism, a closer look at the economic numbers revealed a persistent disparity between projected growth and actual performance.
economic numbers: economic statistics/data
Similar to 'statistical numbers', referring to economic data.
The company's sustained profitability, year after year, speaks volumes about its prudent financial management and consistent growth in key numbers.
consistent growth in key numbers: steady increase in important figures (e.g., sales, revenue)
Refers to crucial financial figures or statistics.
Analysts meticulously scrutinized the quarterly earnings reports, dissecting the complex numbers to identify emerging market trends.
dissecting the complex numbers: analyzing the intricate figures
Used with 'dissecting' to mean carefully analyzing complex data.
The demographic numbers indicated a significant aging of the population, posing considerable implications for social welfare systems.
demographic numbers: population statistics
Referring to numerical data related to population characteristics.
While anecdotal evidence might suggest otherwise, a comprehensive review of the scientific numbers definitively disproved the long-held hypothesis.
scientific numbers: scientific data/results
Used to mean empirical data or measurements in a scientific context.
Collocations courantes
Phrases Courantes
by the numbers
following rules or instructions strictly
do a number on someone/something
to damage or harm someone or something
look after number one
to take care of oneself above others
be in a number of places
to be in several different locations
run the numbers
to do calculations to find out information
without number
too many to count
numbers don't lie
facts and figures are always true
crunch the numbers
to perform calculations, especially a lot of them
add up the numbers
to calculate the total
a number of times
several times
Modèles grammaticaux
Structures de phrases
I can count numbers.
I can count numbers from one to ten.
There are [number] numbers.
There are many numbers on the clock.
What numbers are important?
What numbers are important for your phone number?
Can you write the numbers?
Can you write the numbers one, two, and three?
The numbers show [information].
The numbers show how many people live in the city.
We need to look at the numbers.
We need to look at the numbers to understand the report.
It's hard to remember so many numbers.
It's hard to remember so many numbers, like all the digits of pi.
The numbers indicate [result].
The numbers indicate a significant increase in sales this quarter.
Famille de mots
Noms
Verbes
Adjectifs
Mémorise-le
Moyen mnémotechnique
Imagine a 'Number' wearing a 'B'elt and carrying 'One' apple. This reminds you that 'numbers' is a B1 word.
Association visuelle
Picture a group of people holding up signs with different numbers on them, like a 'number' parade! Some signs could be '1', '2', '3', others could be 'first', 'second', 'third'.
Word Web
Défi
Try to count how many 'numbers' you see around you right now. For example, the page 'number' you're on, the 'number' of fingers on your hand, or the 'number' on a clock. Write down five sentences using the word 'numbers' in different contexts.
Questions fréquentes
10 questionsNumbers are like special symbols or words we use to count things, measure stuff, or even just label things. Think of them as a way to show how much of something there is, or where something is in a list.
Of course! If you have, say, 'three' apples, the word 'three' is a number used for counting how many apples you have.
When you measure your height and it's '1.7' meters, the '1.7' is a number telling you its measurement. Or if something weighs '5' kilograms, '5' is the number for its weight.
Imagine a bus with the number '24' on it. That '24' isn't counting anything or measuring, it's just a label to identify that specific bus route. Similarly, your house number is a label.
Not always! While we often see them as symbols like '1', '2', '3', they can also be written as words, such as 'one', 'two', or 'three'. Both are numbers.
A quantity is about 'how many' – like having 'five' cookies. A position is about where something is in a sequence – like being 'first' in line, or living on the 'third' floor. Both 'five' and 'third' are numbers.
Yes, absolutely! Numbers can be negative, like when we talk about temperatures below zero, for example, '-5' degrees Celsius. That's still a number.
Yes, they are! Fractions, like 'half' or 'one-quarter', are also numbers. They represent a part of a whole, which is a type of mathematical value.
That's a great question! Mathematically speaking, the set of numbers is infinite, meaning they go on forever in both positive and negative directions. So, no, they don't really 'end'.
Understanding numbers is super important because they are fundamental to so many parts of our lives. We use them for telling time, handling money, understanding science, and countless other everyday activities. They help us make sense of the world around us.
Teste-toi 54 questions
Listen to the numbers.
Listen for the number in the answer.
Listen for the bus number.
Read this aloud:
Can you say the numbers from one to three?
Focus: nʌm bərz
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Read this aloud:
What is your favorite number?
Focus: ˈfeɪ vər ɪt
Tu as dit :
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Read this aloud:
Say the number seven.
Focus: ˈsɛ vən
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This is the correct order of the first three numbers.
This sentence correctly states that numbers can be big.
This sentence is a common instruction to count.
Which of these shows numbers?
Numbers are used for counting. 1, 2, 3 are examples of numbers.
If you want to count how many apples you have, what do you use?
Numbers are used for counting.
What comes after the number two?
In a sequence of numbers, three comes after two.
The word 'apple' is a number.
'Apple' is a fruit, not a number. Numbers are like 1, 2, 3.
You can use numbers to say how old you are.
Yes, you use numbers to state your age, for example, 'I am ten years old'.
The number 'five' looks like the letter 'F'.
The number 'five' is written as '5', not the letter 'F'.
Listen for a request for a phone number.
Listen for the opening and closing times of a store.
Listen for the number of books someone has.
Read this aloud:
My house number is twelve.
Focus: twelve
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Read this aloud:
I need three eggs for the recipe.
Focus: three
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Read this aloud:
What is your favorite number?
Focus: favorite number
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Write a short sentence using two numbers to describe something you like.
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Sample answer
I have two cats and I like them very much.
Imagine you are telling a friend about your age. Write a sentence saying how old you are using a number.
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Sample answer
I am ten years old.
Write a sentence using a number to talk about how many people are in your family.
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Sample answer
There are four people in my family.
How many brothers does the person have?
Read this passage:
My address is 123 Main Street. My phone number is 555-1234. I have two brothers and one sister. Our house has three bedrooms.
How many brothers does the person have?
The passage says, 'I have two brothers.'
The passage says, 'I have two brothers.'
How many yellow flowers did the person count?
Read this passage:
I like to count the flowers in my garden. Today I counted ten red flowers and five yellow flowers. That is a lot of flowers!
How many yellow flowers did the person count?
The passage states, 'five yellow flowers.'
The passage states, 'five yellow flowers.'
What is the person's favorite number?
Read this passage:
My favorite number is seven. It's a lucky number! I also like the number one because it's the start of everything.
What is the person's favorite number?
The passage says, 'My favorite number is seven.'
The passage says, 'My favorite number is seven.'
This sentence asks for the identification of numbers on a clock.
This sentence indicates the ability to count a specific quantity of numbers.
This sentence is a request to write a sequence of numbers.
The phone ______ 987654321 is not working.
A phone number is a sequence of digits used to identify a telephone line.
Can you please write down the ______ for me? I need to remember it.
The context implies remembering numerical information, such as a phone number or an address.
She is very good with ______; she can add and subtract quickly.
Being 'good with numbers' means being skilled at arithmetic and mathematics.
Please count the ______ of apples in the basket.
'Number' refers to the quantity or count of something.
The page ______ is at the bottom of each page in the book.
Page numbers are used to indicate the sequence of pages in a book or document.
It's important to learn your basic ______ like one, two, and three.
One, two, and three are fundamental numbers, often among the first things people learn in mathematics.
Focus on the context of 'sheer numbers' and its implications for global challenges.
Consider how 'statistical numbers' are presented and what 'rigorous scrutiny' implies.
Think about 'foundational numbers' in the context of scientific understanding and paradigm shifts.
Read this aloud:
The economic indicators suggest a robust recovery, but the underlying numbers warrant a cautious optimism.
Focus: underlying numbers warrant cautious optimism
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Read this aloud:
While the preliminary figures are promising, it's crucial to acknowledge that these are still early numbers and subject to revision.
Focus: preliminary figures promising crucial acknowledge early numbers subject revision
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Read this aloud:
The demographic numbers in the region indicate a significant shift in population dynamics, posing complex socio-economic challenges.
Focus: demographic numbers region indicate significant shift population dynamics posing complex challenges
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Discuss the philosophical implications of whether mathematical numbers are invented or discovered, citing at least two distinct schools of thought on the matter.
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Sample answer
The debate surrounding whether mathematical numbers are invented or discovered delves into profound philosophical territory. Platonism, a prominent school of thought, posits that numbers exist independently of human consciousness, much like abstract forms, and are thus discovered. This perspective suggests an inherent, objective reality to mathematical truths. Conversely, constructivism argues that numbers are human constructs, invented as tools to categorize and quantify our experiences. This view emphasizes the role of human intuition and logical systems in shaping our understanding of mathematics. The implications of these viewpoints are far-reaching, influencing our perception of scientific truths, the nature of reality, and the limits of human knowledge.
Compose a short essay analyzing the historical evolution of numerical systems, from ancient tally marks to modern positional notation, highlighting how each development impacted human civilization.
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Sample answer
The historical evolution of numerical systems mirrors humanity's intellectual progress, each advancement profoundly impacting civilization. Early societies relied on rudimentary tally marks, sufficient for basic counting but inadequate for complex calculations. The advent of systems like Babylonian cuneiform, with its sexagesimal base, marked a significant leap, allowing for more intricate astronomical and architectural computations. Roman numerals, though widely used, suffered from their lack of a zero and complex rules for large numbers. However, the true revolution arrived with the Indo-Arabic numeral system, introducing the concept of zero and positional notation. This innovation streamlined arithmetic, facilitated scientific discovery, and laid the groundwork for modern mathematics and technology, fundamentally reshaping commerce, engineering, and scientific inquiry.
Elaborate on the concept of 'uncountable infinities' in mathematics, using Cantor's diagonal argument as a central explanatory tool. What are the philosophical ramifications of such concepts?
Well written! Good try! Check the sample answer below.
Sample answer
The concept of 'uncountable infinities' represents a profound and often counter-intuitive aspect of modern mathematics, primarily elucidated by Georg Cantor. Before Cantor, 'infinity' was often treated as a singular, boundless entity. However, Cantor demonstrated that there are different 'sizes' of infinity, some vastly larger than others. His groundbreaking diagonal argument provides a rigorous proof that the set of real numbers is 'uncountably infinite,' meaning it cannot be put into a one-to-one correspondence with the set of natural numbers (which are 'countably infinite'). This proof involves constructing a real number that is not present in any purported complete list of real numbers, thereby revealing a fundamental disparity in their cardinalities. The philosophical ramifications are immense, challenging our intuitive understanding of magnitude and countability. It suggests a hierarchy of infinities, opening doors to deeper inquiries into the nature of mathematical existence and the limits of logical systems, influencing fields from set theory to cosmology.
According to the passage, what is the primary significance of dimensionless numbers in theoretical physics?
Read this passage:
In the realm of theoretical physics, dimensionless numbers play a crucial role in understanding the fundamental constants of the universe. These numbers, such as the fine-structure constant or the proton-to-electron mass ratio, are pure numerical values without units. Their precise values, if altered even slightly, could have catastrophic implications for the existence of stable atoms, stars, and ultimately, life itself. The perplexing question of why these fundamental numbers possess their particular values continues to be a subject of intense scientific and philosophical debate, often leading to discussions on anthropic principles and the multiverse hypothesis.
According to the passage, what is the primary significance of dimensionless numbers in theoretical physics?
The passage states that 'Their precise values, if altered even slightly, could have catastrophic implications for the existence of stable atoms, stars, and ultimately, life itself,' directly linking them to the stability of the universe and life.
The passage states that 'Their precise values, if altered even slightly, could have catastrophic implications for the existence of stable atoms, stars, and ultimately, life itself,' directly linking them to the stability of the universe and life.
What makes Graham's number particularly remarkable, according to the text?
Read this passage:
The concept of 'large numbers' extends beyond mere quantity into the abstract domain of combinatorics and probability. Consider Graham's number, a number so astronomically large that it cannot be expressed by conventional scientific notation or even by iterated powers. Its magnitude is so immense that if every digit of Graham's number were written out, the resulting string of digits would far exceed the observable universe in size. Such numbers typically arise in advanced mathematical proofs, particularly in Ramsey theory, demonstrating the astonishing complexity and scale that pure mathematics can unveil.
What makes Graham's number particularly remarkable, according to the text?
The passage explicitly states that Graham's number 'cannot be expressed by conventional scientific notation or even by iterated powers' and that 'if every digit of Graham's number were written out, the resulting string of digits would far exceed the observable universe in size.'
The passage explicitly states that Graham's number 'cannot be expressed by conventional scientific notation or even by iterated powers' and that 'if every digit of Graham's number were written out, the resulting string of digits would far exceed the observable universe in size.'
How does the passage contrast numerology with mathematics?
Read this passage:
Numerology, an ancient practice, purports to reveal hidden meanings and patterns in numbers, often linking them to human characteristics, events, and destinies. Unlike mathematics, which relies on empirical evidence and logical deduction, numerology operates on symbolic interpretations, assigning specific attributes to individual digits or numerical combinations. While its proponents argue for its predictive power and insight into cosmic order, the scientific community widely dismisses numerology as a pseudoscience, lacking falsifiable hypotheses and demonstrable efficacy. Nonetheless, its enduring appeal highlights a deep-seated human fascination with finding order and meaning in the seemingly random.
How does the passage contrast numerology with mathematics?
The passage states that 'Unlike mathematics, which relies on empirical evidence and logical deduction, numerology operates on symbolic interpretations,' and that 'the scientific community widely dismisses numerology as a pseudoscience, lacking falsifiable hypotheses and demonstrable efficacy.'
The passage states that 'Unlike mathematics, which relies on empirical evidence and logical deduction, numerology operates on symbolic interpretations,' and that 'the scientific community widely dismisses numerology as a pseudoscience, lacking falsifiable hypotheses and demonstrable efficacy.'
/ 54 correct
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