/sci/ - Science & Math

>you can't divide by ze...
https://en.wikipedia.org/wiki/Wheel_theory

You can, depending on the Math. Same for this bullshit 1 = 0.99, it depends on the Math, by using Nonstandard Analysis we'd dive into a different kind of proof

>>9317975
factorial isnt a function, thats invalid

>>9318034
>factorial isnt a function
Wrong.

>>9317975
2/3 = 4/6
2!/3! = 4!/6!
2/6 = 24/720
Nope.

>>9318080
1/1 = 2/2
1!/1! = 2!/2!
1/1 = 2/2

there, I can also make up arbitrary equations. whats your point?

>>9318111
If a proof doesn't work for all cases then it's an invalid proof. Go swallow some glass.

>>9318149
>If a proof doesn't work for all cases then it's an invalid proof.
doesn't necessarily mean the pic is wrong tho

>>9318036
if there's 2 y-values for the same x-value then it's not a function. 0 and 1 both yield 1. You're wrong.

>>9318166
>if there's 2 y-values for the same x-value then it's not a function.
Correct.

>0 and 1 both yield 1.
Those are two x values giving the same y value, brainlet.

>>9318111
>whats your point?
The point is you can't take the factorial of both sides of an equation like that.
>I can also make up arbitrary equations
You're retarded. Coming up with one example where the results are still equal doesn't nullify all the other examples where the results aren't still equal. If you wrongly try to claim multiplication and addition are interchangeable and someone disproves you with the example of 3 + 3 = 6 and 3 * 3 = 9, it isn't a valid counterargument to point out 2 * 2 = 4 and 2 + 2 = 4.

>>9318160
>doesn't necessarily mean the pic is wrong tho
What? That's exactly what it means.

>>9318172
but i showed how it works sometimes, so maybe it works in case 1/0 too

>>9318149
>Go swallow some glass.

other anon is b8ing

>>9318180
>it works sometimes
Broken watch theorem

>>9317975
the fact that you are getting 2 values of x should tell you right off the bat that you are not dealing with a well defined function.

>>9318425
sqrt(9) = +3
sqrt(9) = -3

>>9318485
and square roots are not a well defined function, that's why we use principle square roots in applications, so your point?

>>9318488
then im just gonna use principle factorials

>>9318180
>it works sometimes
No it doesn't. 1!/1! being equal to 2!/2! isn't because factorials of numerators and denominators preserve equality, they're just a coincidental case where the factorials of numerators and denominators are equal, like how 2+2 coincidentally equals 2*2 even though multiplication and addition aren't actually the same thing.
>>9318193
>I was just pretending to be retarded.
Fuck off.

>>9318500
>it's doesn't fit my agenda so im just gonna call it "coincidence"
ok
>multiplication and addition aren't actually the same thing.
but multiplication is just repeated addition

>>9317975
The mistake here is in line 1 where you assume that 1/0 is defined by equating it to x and then operating on x. Of course you got a nonsensical result. Therefore, 1/0 is undefined.

>>9317975
You're close
[eqn]
\frac{1}{0} = x \\
1 = 0x \\
\frac{1}{x} = 0 \\
\frac{1}{x} + 1 = 0+1 \\
\frac{1+x}{x} = 1 \\
1+x = x \\
1+x -x = x-x \\
1 = 0
[/eqn]
If we then plug that into the original equation
[eqn]
\frac{1}{0} = x \\
0 = 1 \\
\frac{1}{1} = x \\
1 = x
[/eqn]
And that's our final answer

>>9317975
>Treating factorial as if !/! Is equal to 1
>Thinking factorials can be distributed across the numerator and denominator

Sure Is brainlet season

I like how math went downhill like 400 years ago and never recovered. Now its just proofs for arbitrary things that everyone already accepted as defacto, or shit like x=y via unintelligble nonsense.

>>9319359
That post was unintelligible nonsense.

>>9318166
Retard

>>9318166
>y=x^2 is not a function cause (-1)^2=1^2

>>9317975
>[math]\left(\frac{n}{k}\right)! = \frac{n!}{k!}[/math]
jesus christ

>>9320011
>mfw people on this board can't see great math when it's right in front of them

>>9318111
nice trips but lemme explain why OP's pic is absolutely wrong :
at the second line, a supposition is made, that the gamma function (because OP also admits implicitly that x is real, and well defined in the domain of the gamma function, extension of the factorial to most reals) preserves quotients, as in [math](\frac{x}{y})!=\frac{x!}{y!}[/math], if that was true in the domain of gamma, that would mean the following :
[math](\frac{x+1}{x})!=\frac{(x+1)!}{x!}=x+1 \\
\Longleftrightarrow x+1=(1+\frac{1}{x})![/math]
a relation which clearly doesn't respect the continuity of the function, so nope, the argument made in this pic is doubly wrong

>>9318111
nice trips but lemme explain why OP's pic is absolutely wrong :
at the second line, a supposition is made, that the gamma function (because OP also admits implicitly that x is real, and well defined in the domain of the gamma function, extension of the factorial to most reals) preserves quotients, as in [math](\frac{x}{y})!=\frac{x!}{y!}[/math] if that was true in the domain of gamma, that would mean the following :
[math](\frac{x+1}{x})!=\frac{(x+1)!}{x!}=x+1 \\
\Longleftrightarrow x+1=(1+\frac{1}{x})! [/math]
a relation which clearly doesn't respect the continuity of the function, so nope, the argument made in this pic is doubly wrong

>>9319777
[math]f(x)=x2[/math] is well defined as a function, it's just not an injection

Jesus christ you guys are retards...
obviously factorial is a group homomorphism on the division group of Q...

>>9318034
f(x) = x!
There you go, now factorial is a function.

>>9318166
Kek, that's gotta be embarrassing.

>>9320614
what's the domain and codomain?

>>9320614
If you actualy want to use factorial in a serious way you could at least use the gamma function so it works on reals and complex numbers too.