Why is a negative number an integer?

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So I was in the shower listening to a podcast where one of the host brought up the word integer.

I feintly remembered what an integer is from grade 7 but just to double check I googled it.

Google stated: “An **integer** (from the Latin **integer** meaning “whole”) is colloquially defined as a number that can be written without a fractional component. For example, 21, 4, 0, and **−2048** are **integers”**

I get the basic idea that it’s a whole but why are negative numbers considered an integer? 1 is a whole thing, if you have a whole pizza you have 1 whole pizza that can be divided into slices, but it can’t go less than 1, so if you have a 0 that’s the lowest it goes because there is nothing and any negative number is a theoretical number.

If 0 and anything lower than zero is less than 1, how can it be a whole if it is less than a whole? 0 is the lowest possible number that can divide into every number because nothing is taken away, you can divide with negative numbers but you can also divide with fractions so that doesn’t prove negative numbers as integers. If an negative number is less than a whole because it’s less than zero I feel like that should define it as a fraction.

I feel really silly for making that statement but the more I think about it the more confused I feel i’m making myself, does anyone have any answers?

In: Mathematics

12 Answers

Anonymous 0 Comments

An integer is by definition one whole number – just a plain old number, with no decimals after it, no fraction, nothing irrational like Pi or the square root of two. This includes negative values. -1 is still a ‘whole’ number, you have one whole, complete -1.

The best way to think of it is to separate a number’s *magnitude* from its *sign.* The magnitude of a number is simply how big a number is, no matter if its positive or negative. -5, for example, has the exact same ‘magnitude’ as +5: It’s just that -5 goes the other way. If you have five less stuff rather than 5 more stuff, you’re still working with a 5, right? -5 is as negative as +5 is positive, so we say that they have the same magnitude, but a different sign [+ or -].

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