Q: How many elements are there in a set of real numbers less than 4?

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The complement of a set refers to everything that is NOT in the set. A "universe" (a set from which elements may be taken) must always be specified (perhaps implicitly). For example, if your "universe" is the real numbers, and the set you are considering is 0

The grouping in which the numbers are taken does not affect the sum or product.

This depends entirely on what you mean by numbers. Assuming you mean numbers in the set of naturals or integers, there are 899 numbers in the interval (100,1000).If on the other hand you mean how many increasing rational numbers there are between 100 and 1000, the answer is, infinitely many. The same thing goes for the increasing numbers in the reals, again there are infinitely many numbers.As a side note: due to a property of the real numbers, there are infinitely many more real numbers counting from 100 to 1000 than there are rational numbers. The proper way of saying this is that, relative to the set of real numbers, the set of rationals is a null set. In other words, even though the set of rationals has an infinite number of elements, when compared to the set of real numbers, the set of rationals has relatively no elements at all.

It's a set with an infinite quantity of elements, like the set of all real numbers, or the set of all real numbers except zero, etc.

There are two real numbers and infinitely many complex numbers.

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The complement of a set refers to everything that is NOT in the set. A "universe" (a set from which elements may be taken) must always be specified (perhaps implicitly). For example, if your "universe" is the real numbers, and the set you are considering is 0

By its very name .. it is UNDEFINED. Even in the Extended Real Number set containing +-infinity these elements are UNDEFINED.

Rational numbers and Real Numbers. The multiplicative inverses of integers are not integers.

There are an infinite amount of numbers less than -6

The grouping in which the numbers are taken does not affect the sum or product.

This depends entirely on what you mean by numbers. Assuming you mean numbers in the set of naturals or integers, there are 899 numbers in the interval (100,1000).If on the other hand you mean how many increasing rational numbers there are between 100 and 1000, the answer is, infinitely many. The same thing goes for the increasing numbers in the reals, again there are infinitely many numbers.As a side note: due to a property of the real numbers, there are infinitely many more real numbers counting from 100 to 1000 than there are rational numbers. The proper way of saying this is that, relative to the set of real numbers, the set of rationals is a null set. In other words, even though the set of rationals has an infinite number of elements, when compared to the set of real numbers, the set of rationals has relatively no elements at all.

NO for Integers NO for Real Numbers proof 1 * any integer is not bigger than that integer nor is 0 * any integer. proof for Real Numbers is easier any real < 1 * any real > 0 is not larger than the second Real for example .5 * 1 = .5 is less than 1 or .5 * 2 = 1 less than 2 or .5 * = 1 less than 2 or -1 *3 = -3 less than 3 so all fractions times a positive Real is less than that positive Real All negative numbers times a positive Real is less than that positive Real and 0 or 1 times all positive Reals is also less than that positive Real NO NO NO is the answer

Many options - e.g. -2"Real number" means all the numbers we know, including positive and negative numbers.The only numbers that are not included are "imaginary numbers" - numbers that have an imaginary part i (used only i physics or high mathematics).See real-number

It's a set with an infinite quantity of elements, like the set of all real numbers, or the set of all real numbers except zero, etc.

There are infinitely many: 29, 28, 27, ... 1, 0, -1, -2, -3, ...If you only want non-negative numbers, there are also infinitely many, since there are infinitely many fractions in an interval of any size. And if you include real numbers, you get an even larger (a so-called "uncountable") infinity.

Real numbers are all numbers. So the answer would be -4 and every number after that in the negative direction. So any number that is less than -4. So, -5, -6, and so on.

It cannot be. The cardinality of the set of real numbers is the Continuum. This is greater than the total number of sub-atomic particles in the universe!