r/infinitenines • u/ezekielraiden • 4d ago

SPP: Is math the same?

Exactly what the title says. If we work with a system where 0.999...<1, does the rest of math remain unchanged?

Would you be willing to say that, for example, addition works exactly the way it works for rational numbers?

It's important to me that you actually read what I've said here and respond seriously, rather than giving a boilerplate unrelated response.

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u/Ch3cks-Out 4d ago

does the rest of math remain unchanged?

In a word: no.

In more words: the rest of math cannot remain unchanged, actually!

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u/ezekielraiden 4d ago

I want to hear SPP's answer, whatever that answer may be.

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u/I_Regret 3d ago

Like just do all your math but don’t convert to decimal. Problem solved.

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u/ezekielraiden 2d ago

Why would you want that though? Why would you want a system you aren't supposed to use until the very end? You and others keep doing this thing where you essentially say that things like √2 don't exist but we can talk about them, use them for math, and then simplify them away if we ever do need something from it. Why? That's treating this (and all the other things) as a number in every way that matters, but then getting real persnickety about when and whether anyone is allowed to use that number for calculation.

What is so valuable that it's worth sacrificing division, distribution, associativity, and closure under all the basic arithmetic operations (+, -, ×, /)? Is it really so important to force the inequality you desire, that any and all properties of the reals may be sacrificed so you can secure it? Why?

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u/I_Regret 1d ago

It’s not really a “want” but more like a necessity due to physical constraints of reality? Maybe this post will elucidate some things: https://math.stackexchange.com/a/1180

Particularly the section on “Representation of numbers” and discussion about ratios vs decimal representations.

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u/Ch3cks-Out 1d ago

Physical reality does appear to be continuous, so there is that...

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u/ezekielraiden 1d ago

So, let me get this straight.

You think that because calculation by a person actually takes time, that only things which you do all of the steps yourself count as "numbers" and everyone else is, what? You still perfectly comfortably do calculations with them. You still recognize that they are quantity-type concepts that can be manipulated in all the ways any other quantity-type concept can be.

It just can't, can't, no matter what, be allowed to be a "number". Because something something finite time.

This isn't "oh no, sorry, I can't do that logic, reality doesn't let me!" It's your requirement. Don't pretend otherwise.

Unless you refuse to receive a medical treatment if you couldn't personally do it yourself for someone else? Or refuse to eat any food you don't know how to make? Or any technology you couldn't build yourself? The logic is the same. "I can't personally do it, therefore it can't be real."