# Are there any integers between 0 and 1

- Are there any integers between 0 and 1? Explain
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## Are there any integers between 0 and 1? Explain

There is no integer between 0 and 1. This fact can be proven using the well- ordering principle, which states that any non-empty set of positive.

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0 and 1 are integers (whole numbers) anything between them would have to be a decimal e.g. so no there is no integers between 0 and.

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The intuitive explanation of the proof is as follows: One of the fundamental properties of the positive integer s also known as the natural number s is that any nonempty set of them has a least element. Compare this to the set of all integer s--The negative numbers , a subset of all the integer s, has no least element. This means that, unlike all the integer s, which go to negative infinity , the positive integer s "stop" at some point, at least in the direction of small numbers. So what is that least element of the positive integer s? Assume it is z , an element smaller than 1. But if we square z to get z 2 , another positive integer smaller than 1 and, indeed smaller than z.

An integer from the Latin integer meaning "whole" [note 1] is a number that can be written without a fractional component. The set of integers consists of zero 0 , the positive natural numbers 1 , 2 , 3 , Z is a subset of the set of all rational numbers Q , in turn a subset of the real numbers R. Like the natural numbers, Z is countably infinite. The integers form the smallest group and the smallest ring containing the natural numbers. In algebraic number theory , the integers are sometimes qualified as rational integers to distinguish them from the more general algebraic integers. In fact, the rational integers are the algebraic integers that are also rational numbers.

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Find the sum of all even integers between 101 and 999.

## Are there any integers between 0 and 1? ?

By using our site, you acknowledge that you have read and understand our Cookie Policy , Privacy Policy , and our Terms of Service. Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. It only takes a minute to sign up. My question is how can you even start this proof? I checked the book and google for a formal definition of integers, but they are pretty vague.

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## 3 thoughts on “Are there any integers between 0 and 1”

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Andrew M. answered 09/14/ Mathematics - Algebra a Specialty / F.I.T. Grad - B.S. w/Honors. Integers are whole numbers: positive, negative.