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
If -2 was a fraction then if you had -2 + 4 you woud have a fraction plus a whole number. Since adding a fraction to a whole results in a fraction that would mean positive 2 is also fraction, so the existence of whole numbers proves the existence of negative non-fractional numbers.
Today, mathematicians accept many different concepts as numbers:
– (a) Counting numbers. 1, 2, 3, 4, and so on.
– (b) Fractions: 1/2, 15/4, lots of others
– (c) Negative counting numbers: -1, -2, -3, -4, and so on.
– (d) Negative fractions: -1/2, -15/4, lots of others
– (e) Zero: 0
– (f) Irrational numbers: sqrt(2), pi, e, lots of others
– (g) Imaginary numbers: sqrt(-1), lots of others.
– (h) Complex numbers: sqrt(-1)+1, lots of others.
Mathematicians have mostly standardized names for particularly useful categories of numbers:
– Natural numbers: (a)
– Integers: (a) (c) (e)
– Rational numbers: (a) (b) (c) (d) (e)
– Real numbers: (a) (b) (c) (d) (e) (f)
– Complex numbers: (a) (b) (c) (d) (e) (f) (g) (h)
So to answer your question,
> why are negative numbers considered an integer?
The answer is that the word “integer” is *defined* to include negative numbers. Your question is kind of like asking why, if dogs are mammals, a cat is also considered a mammal. It has something to do with having certain kinds of similar characteristics, but it also has something to do with how the word “mammal” is defined.
If you want to talk about a narrower category that includes dogs but not cats, that might be a fine and interesting category to consider. But really in that case, “mammal” would be the wrong word to use to describe the category of animal you’re talking about.
“Canines” or “canid mammals” would be the term you’re searching for. In mathematics, your more specific term would be “Natural numbers” or “positive integers”.
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