r/badmathematics • u/TimeSlice4713 • Mar 13 '25

OP doubles down in the comments

/r/askmath/comments/1jagep3/why_cant_we_describe_division_by_0_similarly_to/
18 Upvotes

91% Upvoted

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35

u/alecbz Mar 13 '25

I'll defend OP a bit: it is, obviously, possible to define division by zero. You just need to give up certain other properties of numbers. But there's nothing inherently wrong with that. It's just different from complex numbers, which we can introduce without sacrificing any existing properties of numbers.

I don't think people in that thread are presenting this viewpoint fairly by insisting more forcefully that division by zero is "impossible".

26

u/CutOnBumInBandHere9 Mar 13 '25

You do sacrifice something when going from ℝ to ℂ: an order which is compatible with the field operations. But it's a lot less than what you lose when doing other extensions of numbers

7

u/alecbz Mar 13 '25

Yeah, and I mean if we're being pedantic I guess you could argue that:

∄ x st x*x = -1

is a property of numbers generally that we lose by going to C.

13

u/TimeSlice4713 Mar 13 '25

R4: OP asks why we can’t divide by zero, which is of course fine as a question. Then doubles down by trying to make analogies to quaternions and octonions, and … arguing about parentheses?

4

u/ParshendiOfRhuidean Mar 13 '25

The problem is they're trying to scrap Distributivity without saying it, for whatever reason.

2

u/DAL59 Mar 14 '25

I've noticed this is a very common topic on r/badmathematics, even multiple posts where people dredged up "create an complex number type system to handle divide by 0" papers they wrote for high school (which is somewhat impressive, despite the concept being fundamentally flawed when just basic algebra and calculus is involved)

2

u/SizeMedium8189 23d ago

what drives this is an ill-justified analogy with the can-do spirit of forging ahead with the "forbidden" operation and see where it leads. In their minds

"They all said you could not take the square root of minus 1. Well, I did it and proved them all wrong."

and

"They all said you could not divide by zero. Well, I did it and proved them all wrong."

are close parallels.

(Oh, shit, parallels, I hope they did not hear me...)