Why isn't 0/0 defined? Isn't it just equal to one?

why not just make a new symbol for 1/0. that's what they did with the negative square root and it turned out pretty good.

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>>8837699

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>>8837711
Since 1+0+1+0+1... is equal to 1/2
Wouldn't it stand to reason that 1/0 is equal to 0 ? Since it is the average of infinity and negative infinity.

>>8837711
This has been done in various ways. There are a lot of choices you have to make that lead in different directions. You must sacrifice associative multiplication to go down these paths, however.

>>8837699
Not sure if you're trolling but depending on how one approached 0/0 you can get different results. If the numerator approaches 0 faster than the denominator then it will be 0. If the reverse of that, infinity. If the rates are comparable it can be literally any real number.

>>8837699
>Blue Chiyo
OHSHIT
I miss those threads though.

Oh yeah I remember some faggot from here that actually said something like "complicated numbers" that was 1/0.
Shitter made me laugh for the whole day with this autism drawings

>>8837699
Assume 0/0=1
Then 2*0/0 = 1
So 2 = 0/0*1 = 1

>>8837716
Stupid rulings like this are why I don't play 5th.

>>8837847
You can't have that a(x/y)=(ax)/y with 0/0=1. It's like the contradictions that come from using square roots of complex numbers incorrectly.

0/0 = 0 * (any number/0) = any number

>>8837699
>doesn't understand calculus
brainlets OUT

>>8837699

0 is a placeholder symbol for nothing. You cant divide nothing with nothing and have it equal to one.

>>8837722
>Since 1+0+1+0+1... is equal to 1/2
Your currymath is not valid here.

>>8837847
No, 0/0 = 1
Therefore 2*(0/0) = 2
Everything works.

>>8838005
By 0/0, I mean the function x/x. Which will always equal 1 even in x is equal to zero.

>>8837999
0/0 = 1
therefore 0/0 * any number = any number

>>8838010
How narrow-minded can you get? People used to think negative roots were impossible, hell people used to even think negative numbers were wrong hence the term, "negative".

>>8837776
I'm talking about the function x/x which will always be one which technically would allow for 0/0.

>>8837756
Examine the function x/x as x approaches 0. Oh right, it's equal to one. By allowing this, we can use this property to simplify certain equations.

>>8837711
Isn't the symbol for 1/0 just the "90 degrees 8" symbol?

>>8838230
But 2*(0/0) = (2*0)/0 = 1

>>8838528
Then let K = 0/0 = 1

2*K = 2

>>8838528
That identity doesn't work in the 0/0=1 number system.

>>8837699
Because then Integers wouldn't be a ring, and Rationals and Reals wouldn't be a field.

https://en.wikipedia.org/wiki/Ring_(mathematics)
https://en.wikipedia.org/wiki/Field_(mathematics)

>>8838601
https://en.wikipedia.org/wiki/Wheel_theory

>limit of 1/x as x approaches 1 is 1
>1/1 is 1

>limit of 1/x as x approaches 2 is 0.5
>1/2 is 0.5

>limit of 1/x as x approaches 0 is infinity
>HURR DURR 1/0 IS UNDEFINED

the answer is staring right at you, you fucks

>>8838686
>>limit of 1/x as x approaches 0 is infinity

https://www.wolframalpha.com/input/?i=plot%5B1%2Fx%5D

really tickles those brain cells

>>8837699
assuming 0/0=1 then it follows 2=2*0/0=(0*2)/(0*1)=0/0
so we have 1=2.

This is a contradiction.

>>8837711
>why not just make a new symbol for 1/0.
Because then [math]\mathbb R[/math] is not a field anymore.

>>8837722
>equal to 1/2
WRONG

>>8838686
>>limit of 1/x as x approaches 0 is infinity
WRONG. The limit does not exist.
Infinity is NOT A NUMBER and especially not a REAL NUMBER.

>>8838825
I am NOT A NUMBER, I AM A FREE MAN.

>>8838825
>>limit of 1/x as x approaches 0 is infinity
>WRONG. The limit does not exist.
It's not unreasonable to say "the limit of a function at a point is infinity" if the function increases without bound on both sides of that point. 1/x doesn't do that, though.

>>8838825
>Infinity is NOT A NUMBER and especially not a REAL NUMBER.
But it's an element of the closure of the set of real numbers.

>>8838825
if 1/0 would make reals not a field anymore, you could say that 1/0 is an unreal number (Я)

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>>8838860
>>8838825

Infinity is NOT A NUMBER, IT'S A FREE MAN

>>8838907
We have a word for that
"The function is unbounded"
More concise and succinct than the misleading (if not outright false, according to the rule of universal instantiation) claim that
"the limit of the function (exists and) is infinity"

>>8838246
You can't just plug in numbers, find the limit as the function approaches infinity.

>>8838907
This is wrong.
The limit exists, it is infinity.
By convention, we say the limit diverges to infinity.

Compare this to limit as x-> infinity of (-1)^x
This does not converge to any number
It does not diverge to infinity
This limit does not exist

>>8839607
1/x doesn't have a limit at x->0. approaching from left, it goes to negative infinity. approaching from right, it goes to positive infinity. so, it has no limit there.

>>8839613
Depends on how you extend the real numbers. The extended real line distinguishes [math]+\infty[/math] and [math]-\infty[/math] so 1/x is discontinuous at 0, while the projective real line has [math]\infty = -\infty[/math] so 1/x is continuous and equal to [math]\infty[/math] at 0.

If you say 0/0=1 then 0/0=63 also as:
0=63x0
0=0
Therefore 0/0 can be defined as any part of the universal set by this logic.

>>8839839
This board is so mathematically illiterate that it took until now for someone to mention the extended reals.

>>8839850
And this person continues to complain about a problem that has already been addressed.