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

A fraction is a number that can be defined by division. You cannot divide a positive number by another positive number and result in a negative number. Integers can be thought of simply as whole steps starting from 0 your first step to the right is 1, conversely to the left would be -1.

You’re correct that negative numbers don’t exist in nature, they are more used as relational values. To use your pizza example. If you start with 5 pizzas and someone eats 2 of them, you have 3 pizzas left. The missing pizzas could be represented as a negative 2 pizzas, if they were whole numbers before they were taken away, why would they be fractions when they are missing?

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