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
The absence of a thing is a thing in and of itself. So if you have an absence of a whole amount, that’s negative one things.
Instead of thinking as Zero as the absence of a thing, think of it as a lacking of any things, including absence. Zero is just a concept of nothingness. No-Thing-ness.
Does that make any sense? I’m not entirely sure, just thought I’d throw that out there.
It sounds like you’re confusing whole numbers and integers. A whole number is all positive numbers without a fractional component and zero, like 0,1,2,3… (and there’s technically another subset called natural numbers that don’t include zero), while an integer includes all whole numbers and their opposites (read: throw a minus sign in front of each number)
You’re confusing whole numbers vs rational numbers with positive vs negative.
A whole number is one that does not have a decimal or fraction (eg 10 is whole but 10.5 or 10 1/2 are rational)
A positive or negative number can be whole or rational.
because the WHOLE pizza is missing at -1. It is not a fraction of a whole it is the whole thing.
Stop thinking of negative numbers as something not being there –
In [mathematics](https://en.wikipedia.org/wiki/Mathematics), a **negative number** is a [real number](https://en.wikipedia.org/wiki/Real_number) that is [less than](https://en.wikipedia.org/wiki/Inequality_(mathematics)) [zero](https://en.wikipedia.org/wiki/0_(number)). Negative numbers represent opposites. If positive represents a movement to the right, negative represents a movement to the left. If positive represents above sea level, then negative represents below sea level. If positive represents a deposit, negative represents a withdrawal.
TIL integer is not a programming exclusive word. As a non native, I’ve only seen it being used in programming context, so I assumed only programmers use it to describe numbers, like float or double.
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 -].
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?
> An integer (from the Latin integer meaning “whole”) is colloquially defined as a number that can be written without a fractional component.
What is the fractional component of -1?
Nowhere.
Ergo, it satisfies the definition criteria, and is an integer.
The same cannot be said about -1.456, because you can see that -0.456 fractional right there.
It seems like you’re making up your own definition of integer. You say it has to be a whole number, which is not true. It can’t be “theoretical”, whatever that means. You say you must be able to divide it into every number, which is also not true. You’re then confused why there are integers that don’t match your definition.
An integer is simply a number in the set { … , -4, -3, -2, -1, 0, 1, 2, 3, 4, … }. The dots “…” indicates that the set goes on forever in both directions. You can see how all these numbers can be written without fractions. That’s all there is to it.
Consider this: 70-69 = 70+(-69) = 1.
-69 is an integer and part of the whole (70). So your assumption that any integer less than 0 is less than a whole is incorrect. You see, we can make any negative integer part of a whole if we wanted to. You are thinking about numbers in a specific way, forget about “wholes”. It is better to look at it as movement along a number line. You can have $5, be charged $10 and then have a balance of -$5.
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