1/0=infinity

1/0=infinity
Prove me wrong.

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infinity=1/0=1/(-0)=-1/0=-infinity

1/0 = every number simultaneously

The proof is trivial.

Assuming the axiom of infinity, the following holds trivially.
[math]\epsilon_0= \kappa^{\lambda^\infty}0 = 0 \iff 1 / 0 = \infty [/math]

Using the universal property of [math]\epsilon_0[/math] we trivially obtain
[math]\forall n, \, 0 \cong \pi_{n + \lambda}(S^n) \, /\ \mathbb{Q}^\infty \otimes (\mathbb{Z}^\infty * \mathbb{Z}^\infty)[/math] which is a contradiction.
[math]\blacksquare[/math]

Exactly, that's why we say it's undefined.
6/2=3, because 3*2=6
10/5=2, because 5*2=10
1/0=0, because 0*0=0
1/0=1, because 0*1=0
1/0=2, because 0*2=0
1/0=3, because 0*3=0
etc.

>1/0 = x
>(1/0)*0 = x*0
>1 = 0*x
>1 = 0

math is a tool created by man. You can't divide by zero in the same way you can't measure the weight of something with a tape measurer.

What if you hung the weight off the end of the tape and measured how far it got pulled out against the rewind spring

infinity is not a number,but a concept.
dont make sense

/thread

Uzumaki was a pretty good.

what is negative zero outside computing?

sounds like infinity to me

>infinity is not a number,but a concept.
>numbers are not concepts
pray tell, what might they be?

1/0 = infinity
infinity * 0 = 0
1 != 0

>1 != 0
Prove it.

If you multiply 0 by infinity you don't get 1, as simple as that.

>what might they be?
Depends on what formalism you are using.
An operation called "division" being defined on "infinity" is non-standard. Specify exactly what you mean by "infinity".

>multiply 0 by infinity
How does one "multiply by infinity"? Sounds like unrigorous gibberish to me.

Wrong.

You got that backwards.

6/2 = 3 because 3*2 =6
10/5 = 2 because 2*5 = 10
but
1/0 = ??? (no answer), undefined because there is no number that you can multiply by 0 to get 1.
But
0/0 = ??? (anything), undefined because it can be literally any number n * 0 = 0

tl;dr 0/0 and 1/0 are both undefined but for entirely different reasons

>used trivial in every sentence before every result

infinity isn't a quantity you fucking dolt

>t. engineer

This wouldn't work. Any weight that was strong enough to pull out the tape at all would pull out all of the tape. (Given room.)

if it was,

1/0 = 2
1 = 2*0
opposite from what you said, not every number, not a single number satisfies 1/0 = x

where exactly is the error in this again?

between the 4th and 5th line where (a - b) is removed.
You divide both sides by (a - b), which is not allowed, since a - b = 0
If division by 0 was infinity this would be a legit operation

abs(x/y) is defined if and only if x OR y is non-zero.
sign(x/y) is defined if and only if x AND y are non-zero.

literally an axiom

>[math]\infty\cdot 0=0[/math]

en.wikipedia.org/wiki/Riemann_sphere
You're not wrong.

Only in some very crippled system.

This is a misunderstanding of the division operator.

While you may have been taught in grade school that you can visualize division by literally dividing a quantity into parts, this is not how we define division.

a/b=c means c is a number, which when multiplied by b equals a. This is the only meaningful definition of divison, and inherently rules out infinity as an answer

Those who better understand mathematical statements correct me on this, but I'm pretty sure 1/0 is undefined because the limit of 1/x as x approaches 0 is -infinity when approaching -0 and +infinity when approaching +0, which contradicts itself because -infinity=/=+infinity, meaning that 1/0, in the form of a the limit x->0 1/x is undefined

This is equally wrong.

Holy shit you stupid fuck a/b=c so b*c=a so
1/0=0 would mean 0*0=1 it's no numbers not every number

> 1/x = 1/-x

1/0 = inf/1
0/1 = 1/inf

An infinite number of zeroes would still sum to zero.
0+0 = 0 ALWAYS

That really depends on the infinity.

>put nothing into a box
>how long until the box is full

>"-infinity=/=+infinity"
Pop-sci garbage.

But isn't the internal mechanism of a tape measure based upon a spring/coil? Wouldn't the resistance become stronger as it tightens due to the weight?

The proof is indeed trivial.

Infinity = -infinity

Except it doesn't, because n^x and n^-x approach very different values when x approaches infinite.

do you want -infinity money?
you will be rich ;)

what if I use an extension of the real number system such that it is [math]\mathbb{R} \cup \{\infty\} [/math]
constructed with the analytic extension such that any divergent series tends to [math]\infty[/math]?

The visual would be a circle with infinite radius representing an extension of the reals.
now that I have concocted this bullshit extension, OP is suddenly right.

t. algebraic analyst

this got me thinking about some universal property for one-point compactification and I ended up at the nlab page for "compactum space". I kekked a bit

>infinity=-infinity
nothing wong with that
lrn2projectivegeometry, plens

That's 0/0
Prove yourself right

1/0 = 1

>complicating basic point-set topology with tumorous category theory
It's like I'm watching Haskellfags in /g/ try to write fizzbuzz using hundreds of lines of boilerplate.

I think he meant that multiplaying any number (so in the range of infinity?) With 0 will not result in an answer of 1

stop using hookes law

Infinity can be positive or negative and since zero is neither we don't know which one it is chromate atheists

You're pretty good.

>algebraic analyst
So in other words a subhuman?

>an extension of the real number system
That would first require the real number system to actually exist.

>/g/
Subhuman engineer spotted.

1/0 = 1, because 0 means nothing, nothing is being used