Following on from my thread where I got wrecked for being brain damaged, and posting about dividing by zero, it is time for round two!
Lightening round: Electric boogaloo!
Episode 3: "Glutton for punishment"

You can read that thread here if you like or skip over.
https://devrant.com/rants/4931841/...

Can we divide by zero? Is there some representation where thats the case? And what are the implications if we can?

In this round Devranters, you will be challenged to determine if OP is 1. insane, 2. a genius, 3. high on mushrooms. One contestant will be eliminated. The winning team will get a bag of rice and sunscreen, while the other team will have to vote to send someone home from the island.

Get ready.

Heres the full rant because DR wouldn't post it for some reason:

https://pastebin.com/qBg80ujN

Division isn't a basic mathematical operation. Basic operations are multiplication (with a scalar) and addition (subtraction is just addition with negative numbers). Division isn't a part of that. It doesn't exist in number theory, it doesn't exist in most fields of mathematics actually.

Division is a theoretical inverse of multiplication, not a mathematical operation, and it's only defined as such, i.e. "Can we find a number such that x*0=5?" "No" is a perfectly valid answer to that question. And that's what division is all about.

@hitko This is even more obvious when it comes to vector spaces (or linear algebra in general): Can we find a number such that x*[1,2,3] = [2,-3,5]? No, because those two vectors don't have the same (or opposite) direction. "No" is a valid answer.

@atheist

> there are different types of infinity

I always forget that detail.

If this were in a chemistry lab, you would be like "Uhh, thats not a good idea. I don't recommend it."

And then I'd do it anyway, and BOOM.

eyebrows gone, or worse.

@atheist if you look a bit crooked at uncountable infinities like the numbers between 0 and 1, would it be wrong to say they're really just transformations over powers of 10 from the countable infinities of the integer number line?

> j^j represents types of uncountably infinite stuff.

Actually, thats clever. Didn't think of that.

Does it make sense to generally think, of 'inf' not as a specific number, but as a set of numbers, or an operation over the set?

So if you did inf/inf, regardless of the set we're talking about, the result would come out to

[1, 1, 1...]?

Actually it occurs to me that a continuous function is a kind of uncountable infinity, because it covers the set of all numbers that it intersects, not just the integers, no?

> tan(x) lim x-> 0

I'm not at all familiar with calculating limits so I couldn't tell you.

@atheist

> The parallel between root(-1) and 1/0 is there.

Well I'm glad to know I'm not entirely insane.

I think my mistake here is treating 'inf' as an arbitrarily large number, or point. Guilty as charged.

But I 'm not familiar with any other way to represent that relationship between some variable and some other variable that is arbitrary preciseness. or arbitrarily large in value relative to the other.

I mean how do you express that right?

Theres A, and then theres B, and however big B is, its just another number on the line of countable integers for example. But suppose you *did* want to say "this number or set of numbers are so large as to be uncountable in theory and/or practice."

@atheist Imagine for a moment you have

n/0.

N is arbitrarily large.

Now replace plain zero, with k like mentioned before.

n is effectively so large, as to reduce k to zero

if we were to take k/n

As an aside if we're talking about an arbitrarily large point on a line--*arbitrarily large relative* to another point, k, then wouldn't j*j and j^j be distinct? We're treating the arbitrary point as arbitrary because its either an infinite set, or its so large as to be impossible to enumerate

in any amount of time.

If its simply a point without any symbolic purpose, then j*j is obviously reduceable to j^2, but if its a symbol, then it doesn't necessarily have to be the case that j*j == j^2, though that would be convenient for not breaking another convention.

@atheist "Which, if you look at tan (or 1/tan), as x tends to 0, you get a different result depending on if you approach from positive side or negative side."

That behaviors kind of interesting though, makes me wonder what kind of utility it might have, even if its wrong.

What if k is constrained to the same sign as n?

What if k is signless? What are the implications?

> Its been a while since I've done this stuff

Drunk you knows way more than sober me, and I am grateful.

@atheist oh man I'm sorry to hear it.

"We're up all night to get lucky" as the song goes.

And instead we're doing math lol.

Thanks for it all, and thanks for the links.

Sleep well man. Sleep Well.

5/0 is undefined. 5/0 is never *infinity*.

What kind of crazy hole did the writer crawl out from?

My pick: High on mushrooms/weeds

@daniel-wu I'm not high on mushrooms.

I just choose to live in other dimensions sometimes.

@atheist Please don't bring that stupid "calculus for kids" oversimplification form into this. How do you express (-3)*(-5) as a series of additions? You repeat addition a negative number of times? How about 0.5*0.3? You do it 0.3 times? And even if you could do that, how would you express sqrt(2)*sqrt(8) (two irrational number which give an integer result)? Basic mathematical operations aren't defined for discrete values, they're defined based on what happens to every value in the (numeric, vector, ...) space. Addition moves every value in the space by a fixed amount, multiplication stretches the distances between the values by a fixed amount. In these terms, division is asking "Can we unscale the resulting space back into the original?"

The same goes for exponentiation; thinking of it as a series of multiplications is just an oversimplification they teach to children. Mathematically, exponentiation "bends / rotates" the space, and logarithm is like asking "Can we transform it back?"

@hitko All this is what mathematical analysis is about, but I tried to keep it out of this because it's not something most people ever learn about. A fundamental thing to keep in mind is that an operation is only invertible when it preserves the cardinality, e.g. multiplication preserves cardinality unless it scales the entire space into a single value (multiplication by 0).

@atheist They aren't coupled. People who claim they are coupled are people who think that the sum of all positive integers is -1/12, because they never learned mathematical analysis.

@atheist It breaks as you get into negative basis and more complex (e.g. decimal, matrix) exponents and spaces, where you can no longer calculate it as multiplication. Say, what's a^x if a is a negative number? For real x, it's an oscillating series with exponentially increasing amplitude in complex space. What if a is a (square) matrix? There's no such thing as division by a matrix, but the result is still well defined as a new matrix of the same shape.

@atheist Well, a^-1*a = 1 still holds for matrices the same it does for numbers, except that when dealing with matrices, "one unit" (1) is an identity matrix. That's why a^-1 = 1/a (division) only "holds" for basic numerical spaces, while a^-1*a = 1 (multiplication, exponentiation) "holds" for all mathematical spaces.

@hitko On that note, a/3 = b is defined for matrices as an "inverse" to the multiplication by a scalar.

@Wisecrack
@atheist
@-red
& @hitko

I am reading this stuff.
Mumble 'oh no'.
Wife goes 'what's wrong? What's happening??' as if something bad occurred.
I tell her.
'There's people who do heavy maths.
They attempt to divide by zero and then say things like axioms and elementary functions.
And there is this thing with two different infinities.'
She calls bullshit.
Proper slates me.
'There's only one infinity.'
I Google the shit.
Britannica.com says
"there's three different types of infinity."
We decide to go to bed and call it a day.
I'm going to sleep well, fully ignoring all the infinite types of infinities.
Thank you lads =D