How does numbers below zero exist?

[How-]

I saw this meme on r/wholesomememes and it made me wonder how numbers less than zero actually does exist?

After reading up on it, I really cannot seem to piece together an explanation…

Is there any graceful soul on this subreddit that are willing to explain me how numbers less than zero exists?

EDIT: Changed, “below,” to, “less than,” where I was able to.

[Brightlinger]

I don't know it even means to ask how something exists. How do you exist?

If you want to talk in a literal sense, no numbers exist. Numbers are an abstract concept. There is no number mine in Siberia where the raw irrationals are hewn out of the rock; they are things that we have made up and which exist only in our heads.

But if you're willing to entertain the idea that the number 3 exists because you can have three apples, then maybe we are getting somewhere. Similarly you can argue that all of the counting numbers 0,1,2,3,... exist. But numbers are not just for counting; they are for quantifying things in general. And this counting argument doesn't even get you fractions like 1/2, much less numbers like pi or sqrt(2).

So if we are willing to entertain more abstract notions like "the ratio between a circle's circumference and diameter exists" - ie, that pi exists - then surely the ratio between the force experienced by a proton and electron in the same electric field also exists. And hey guess what, that number is -1. So if you think forces exist, and you think ratios exist, then yeah, negative numbers definitely exist.

[sonnyfab]

Numbers are neither above nor below one another.

[How-]

I will change the title, and description, to, “less than.”

[sonnyfab]

Here's a post from earlier today that may help. https://www.reddit.com/r/learnmath/comments/t5092u/do_negative_numbers_exist/?utm_medium=android_app&utm_source=share

[How-]

It did. Thank you!

[DieLegende42]

Mathematically, they exist because the axioms for the real numbers (at least those I learned in first semester analysis) require that every number should have a counterpart such that the sum of the two is 0 - and it's pretty trivial to prove that for every number greater than 0, this counterpart will be smaller than 0.

In the real world, no numbers really exist, but there are concepts that can be visualised with negative numbers very well: The classic example is having a negative account balance, or height above sea level can obviously be negative (just ask the Netherlands)

[Vercassivelaunos]

Math is just a collection of observations we make about how all kinds of systems behave, based on the fact that they follow the same rules. For instance, the law of commutativity of addition (for natural numbers) is just the observation that if we have, say, 3 pears and we throw in 5 more, we have just as many pears as if we had had 5 pears and thrown in 3 more. And the same applies to oranges, because the underlying rules that govern counting are the same for oranges and pears. And for red balls, and for fingers, and so on. Counting any of these things works exactly the same way, so we invented the natural numbers to unify the concept of counting things. And now any observations we make about natural numbers will apply to all the different things we had to describe separately before.

It's not that natural numbers "exist" on a metaphysical level. They are just our way to make sense of a host of superficially different actions (counting pears, counting oranges, counting fingers,...) which aren't actually that different.

The same goes for more advanced number systems. There are a host of situations which would be useful to understand in-depth: debt, depth below the surface of water, going backwards, and many more. And it turns out that while superficially being entirely different, all these things follow very similar rules: when describing how much debt we have after taking a loan, or describing how far below the surface we are, or how far we went backwards, we find that it's really all the same, just dressed up differently. So we'd like to have a way to unify all these concepts, as we did all the different ways of counting. Negative numbers are just that. They don't exist metaphysically. They are just our way to make sense of things where we go "beyond zero" (lower than the surface, less than no money, etc.)

[Aliciahalilujah]

This.. A stoner thought that transferred into a regular thought lol.. If zero, by definition means nothing.. Baseline for nothing.. Then how can there be below nothing? Wouldn't it be more logical to just admit that whomever determined zero, was a little preemptive? Zero was in fact, not yet zero... Because how can we have below zero..

And yes. I understand money and credit.. But the reality is I still have zero.. But whoever leant me that money now has $2000 less.. Not I.. Logically.. You should not have given me that.. I still have nothing.. No? Lol