A classification quiz
by Buddy1.
Estimated time: 3 mins.

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Quiz Answer Key and Fun Facts

Answer:
**Characteristic of Zero**

A cardinal number is a number that is part of a set. If there are five items, then the set could be all integers from zero to five. If you divide an item into five pieces, then the set would be {0, 1/5, 2/5, 3/5, 4/5, 1}. If a set has nothing that is part of it, then it is called a null set and is represented by {0}. If it's a given there are a positive number of items, then zero would not be part of a set. All of this to say that zero is a cardinal number, since it can be part of a set.

A cardinal number is a number that is part of a set. If there are five items, then the set could be all integers from zero to five. If you divide an item into five pieces, then the set would be {0, 1/5, 2/5, 3/5, 4/5, 1}. If a set has nothing that is part of it, then it is called a null set and is represented by {0}. If it's a given there are a positive number of items, then zero would not be part of a set. All of this to say that zero is a cardinal number, since it can be part of a set.

Answer:
**Characteristic of Zero**

A real number is any number that can be used to measure something. This includes intangible items such as temperature and duration as well as tangible items such as the number or size of an object. Zero can be used to measure these things. In some cases, zero means lack of something (like if there are zero number of items) while in other cases, this is not true (like if the temperature is zero degrees; it does not mean lack of temperature).

The opposite of a real number is an imaginary number, which is usually introduced in a calculus class, so any number taught beforehand would be considered a real number.

A real number is any number that can be used to measure something. This includes intangible items such as temperature and duration as well as tangible items such as the number or size of an object. Zero can be used to measure these things. In some cases, zero means lack of something (like if there are zero number of items) while in other cases, this is not true (like if the temperature is zero degrees; it does not mean lack of temperature).

The opposite of a real number is an imaginary number, which is usually introduced in a calculus class, so any number taught beforehand would be considered a real number.

Answer:
**Characteristic of Zero**

An integer is defined as a number without a decimal or a fraction. When you write the number 0, there is no visible decimal or fraction. The number could be written as 0.0, but that still equals 0, so 0 remains an integer. Another way of saying this could be that the "without a decimal or fraction" comes to play if taking the fraction or decimal away changes the value of the number.

In the above examples, taking away ".0" doesn't change the value whereas taking the ".75" away from 8.75 does change the value.

An integer is defined as a number without a decimal or a fraction. When you write the number 0, there is no visible decimal or fraction. The number could be written as 0.0, but that still equals 0, so 0 remains an integer. Another way of saying this could be that the "without a decimal or fraction" comes to play if taking the fraction or decimal away changes the value of the number.

In the above examples, taking away ".0" doesn't change the value whereas taking the ".75" away from 8.75 does change the value.

Answer:
**Characteristic of Zero**

A rational number is any number that can be expressed as either a decimal or a fraction. Rational numbers include whole numbers as well as decimals and fractions. In other words, not only is 3/4 and 0.75 rational, so are numbers like 25 and 0, which can be expressed as 25.0 and 0.0 respectively. An example of a number that is not rational (i.e. irrational) would be pi (3.1415...), Euler's number (2.718) and square roots that don't result in a whole number (like the square root of 3, which is approximately 1.732...) since the decimals go on forever without repeating or stopping.

A rational number is any number that can be expressed as either a decimal or a fraction. Rational numbers include whole numbers as well as decimals and fractions. In other words, not only is 3/4 and 0.75 rational, so are numbers like 25 and 0, which can be expressed as 25.0 and 0.0 respectively. An example of a number that is not rational (i.e. irrational) would be pi (3.1415...), Euler's number (2.718) and square roots that don't result in a whole number (like the square root of 3, which is approximately 1.732...) since the decimals go on forever without repeating or stopping.

Answer:
**Characteristic of Zero**

Whole numbers are defined as the set of non-negative integers. Since zero is not negative, that makes zero a whole number.

Some people say whole numbers and natural numbers are the same but, in mathematics, natural numbers start at one. However, there should be a term for numbers that start at zero since, in some cases, starting at zero is better than starting at one, hence the need for the term "whole number". One instance in which you would start counting from zero is with computer programming due to the way computer memory is structured.

Whole numbers are defined as the set of non-negative integers. Since zero is not negative, that makes zero a whole number.

Some people say whole numbers and natural numbers are the same but, in mathematics, natural numbers start at one. However, there should be a term for numbers that start at zero since, in some cases, starting at zero is better than starting at one, hence the need for the term "whole number". One instance in which you would start counting from zero is with computer programming due to the way computer memory is structured.

Answer:
**Not a characteristic of Zero**

A happy number is any such number where the sum of the square of its digits equals one. Zero is the only digit, and its square is zero. Repeating that as many times as you like will still result in zero. Since zero doesn't equal one, zero is not a happy number.

An example of a happy number is 19:

1^2 + 9^2 = 1 + 81 = 82

8^2 + 2^2 = 64 + 4 = 68

6^2 + 8^2 = 36 + 64 = 100

1^2 + 0^2 + 0^2 = 1 + 0 + 0 = 1

Numbers that aren't happy are called unhappy, so zero is an unhappy number.

A happy number is any such number where the sum of the square of its digits equals one. Zero is the only digit, and its square is zero. Repeating that as many times as you like will still result in zero. Since zero doesn't equal one, zero is not a happy number.

An example of a happy number is 19:

1^2 + 9^2 = 1 + 81 = 82

8^2 + 2^2 = 64 + 4 = 68

6^2 + 8^2 = 36 + 64 = 100

1^2 + 0^2 + 0^2 = 1 + 0 + 0 = 1

Numbers that aren't happy are called unhappy, so zero is an unhappy number.

Answer:
**Not a characteristic of Zero**

Perfect numbers are positive integers equal to the sum of the number's factors, excluding the number itself. As mentioned above, zero is not positive, so it can't be perfect.

Also, a factor is a number that divides the given number without any remainder. Using zero as the given number, any positive number divided by zero gives zero as an answer, so it could be said that every positive integer is a factor of zero, and adding up all the positive integers doesn't result in a sum of zero, and therefore, zero is not a perfect number.

Perfect numbers are positive integers equal to the sum of the number's factors, excluding the number itself. As mentioned above, zero is not positive, so it can't be perfect.

Also, a factor is a number that divides the given number without any remainder. Using zero as the given number, any positive number divided by zero gives zero as an answer, so it could be said that every positive integer is a factor of zero, and adding up all the positive integers doesn't result in a sum of zero, and therefore, zero is not a perfect number.

Answer:
**Not a characteristic of Zero**

Transcendental numbers do not have a root of a non-zero polynomial equation. An example is Euler's number e. There's no equation where you can substitute x in for e, and it works out exactly.

If there is such an equation, then the number is algebraic and not transcendental.

An example of an algebraic number is zero:

x ^ 3 = 0

x = cubed root of 0

x = 0

Most people would define an algebraic number and then say that any number that isn't algebraic is transcendental. This is opposed to the idea of actually giving a definition to transcendental numbers.

Transcendental numbers do not have a root of a non-zero polynomial equation. An example is Euler's number e. There's no equation where you can substitute x in for e, and it works out exactly.

If there is such an equation, then the number is algebraic and not transcendental.

An example of an algebraic number is zero:

x ^ 3 = 0

x = cubed root of 0

x = 0

Most people would define an algebraic number and then say that any number that isn't algebraic is transcendental. This is opposed to the idea of actually giving a definition to transcendental numbers.

Answer:
**Not a characteristic of Zero**

A prime number has exactly two factors: the number one and the number itself. The number zero has no factors or could be said to have every whole number as a factor). Either way, there are not exactly two factors of zero, thus making zero a number that is not prime.

Zero is also not composite. This is because a composite number must have a finite number of factors, assuming that finite number is two or greater, and zero has an infinite number of factors.

Using these definitions also proves that the number one is neither prime nor composite.

A prime number has exactly two factors: the number one and the number itself. The number zero has no factors or could be said to have every whole number as a factor). Either way, there are not exactly two factors of zero, thus making zero a number that is not prime.

Zero is also not composite. This is because a composite number must have a finite number of factors, assuming that finite number is two or greater, and zero has an infinite number of factors.

Using these definitions also proves that the number one is neither prime nor composite.

Answer:
**Not a characteristic of Zero**

Positive numbers are defined as any number that is greater than zero. Since zero is equal to zero, and therefore, not greater than zero, then zero is not positive. Similarly, a negative number is defined as any number that is less than zero. This means that zero is not negative, since if one number is less than another number, then by definition, they can't be equal.

Therefore, zero is neither positive nor negative. Conversely, no negative is both positive and negative.

Positive numbers are defined as any number that is greater than zero. Since zero is equal to zero, and therefore, not greater than zero, then zero is not positive. Similarly, a negative number is defined as any number that is less than zero. This means that zero is not negative, since if one number is less than another number, then by definition, they can't be equal.

Therefore, zero is neither positive nor negative. Conversely, no negative is both positive and negative.

This quiz was reviewed by FunTrivia editor rossian before going online.

Any errors found in FunTrivia content are routinely corrected through our feedback system.

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