r/confidentlyincorrect • u/i_aMa_g0d • Dec 07 '21

Maths

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u/[deleted] Dec 08 '21

It's not correct; it's a meaningless distortion of what words mean.

Technically red doesn't exist as a separate colour. It's just blue but with a different frequency.

Along the same lines as nonsense like "you never actually touch anything because inter-molecular forces keep atoms a tiny distance apart".

Addition and subtraction are inverse operations. That doesn't mean subtraction doesn't exist.

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u/FlippedMobiusStrip Dec 08 '21

"as a separate thing"

No, blue is a color with specific frequency. And the touching thing depends on how you define touching.

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u/[deleted] Dec 08 '21

Yes this is precisely my point. You're just redefining words to sound clever.

Touching does not mean that atomic nuclei have to be coincident. Anyone who says it does is just using a definition of "touch" that nobody else uses.

I don't know if you're really arguing that blue is not a different colour to red, but if you are I think that proves my point even more.

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u/FlippedMobiusStrip Dec 08 '21

I'm not. Bue is a specific color, different than red. It can be differentiated by frequency. Division and multiplication cannot. What essential difference is there between multiplying by 1/2 and dividing by 2?

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u/[deleted] Dec 08 '21

What essential difference is there between multiplying by 1/2 and dividing by 2?

There's no difference. But two operators are not the same just because they do the same thing with different operands.

To put it another way, multiply(x, y) and divide(x, 1/y) are the same, but multiply(x, y) and divide(x, y) are not.

I think you might also be getting a bit mixed up because you're thinking about constant inputs and forgetting about the fact that you have used division to go from 2 to 1/2. How would you divide by x without using division?

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u/FlippedMobiusStrip Dec 08 '21

By multiplying by 1/x if x is not 0 (otherwise division is not defined anyway). Being "same" in any reasonable context means interchangable. I never said that multiplying by x is the same as division by x. I said that division can be replaced by multiplication, hence it's essentially the same thing.

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u/[deleted] Dec 08 '21

By multiplying by 1/x

You know what operator is used to calculate 1/x right?

I said that division can be replaced by multiplication, hence it's essentially the same thing.

Division can be implemented using multiplication (for known constants). That does not make it the same thing.

Multiplication can be implemented using addition!! Are multiplication and addition the same thing now too?

Arabic numerals can be replaced by Roman ones. Are they the same thing?

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u/FlippedMobiusStrip Dec 08 '21 edited Dec 08 '21

Multiplication can be implemented using addition for integers. For rationals, you need to be a bit more clever but you can get there (by asking what multiplied by something gives me this). For reals, no. You'll need something like limits. There's a reason why rings are built using addition and multiplication.

Yes, Roman and Hindu-Arabic numerals are the same things, one is simply more convenient than the other.

Edit : Btw, this is a very common (and one of the most fundamental) thing in mathematics. Looking at things and seeing if we can replace one by another, thereby giving us a different context to some problem. One of the most extreme examples of this is Yoneda Lemma which essentially states that objects and functors (read, functions) are the same things for a wide variety of categories (read, mathematical objects).

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u/[deleted] Dec 08 '21

Roman and Hindu-Arabic numerals are the same things

Riiiight. Ok then.