/sci/ - Science & Math

>>10124605
Define 1
Define /
Define INFINITY
Define =
Define 0

You just answered your own question, pointless thread

>>10124605
Infinite numbers only exist in contexts like ordinal and cardinal arithmetic where division isn't defined.

>Does 1/INFINITY = 0?
No but lim x->infinity 1/x, for all intents and purposes, does

Depends how many sig figs your teacher asks you for.

>>10124605
1/∞ = ε

>>10124605
That's why we use limits.
>>10124611
SURREAL NUMBERS
>>10124819
REEEEEEEEEE

>>10124611
>Infinite
>numbers
choose

>>10124819
I N F I N I T E P R E C I S I O N

1/infinity

1/(1+2+3+...)

1/(-1/12)

-12

Q.E.D.

>>10124605

No because infinity isn't a number

>>10126521
doesn't matter, only if bigness is disputed can you say that

infinite is big. duh

>>10124605
If the universe is infinite, then we are nothing. One person among infinite objects is nothing, right?

Stop thinking of math as having anything to do with physics or the universe.
Math is not limited by or contingent upon this universe or physics - rather, this universe and physics are contingent upon math.

Isn't 1/plus or minus infinity equals to 0^- or 0^+ ?

>>10124621
This, it isnt helpful to think of infinity as a number

>>10124605
It's infinitesimally small but not true zero. Anyone who says so is a wanker.

>>10124605
infinity doesn't real

>>10124605

It literally doesn't equal zero, no matter how big the number on the bottom gets, it can and will never result in an answer of zero. Will it get so close to zero that for "practical" purposes you might as well call it zero? yes. But it does. not. equal. zero.

L I M I T S

>>10124605
It’s increasingly smaller but never 0. You could round it to that just like 1/3 = 0.333~ but 0.333*3 not equaling 1 problem

>>10127493
>the number
>>10126462

>>10127694

infinity is not some magical concept, it's just n+1 forever, and no matter what you want to push it to, it will not make 1/INFINITY zero. the function 1/x has a limit of zero, even if you put infinity as x, it can come very close to but never actually touch zero. Maybe you should take a math refresher course buddy, if you actually think it equals zero. Once again, for practical purposes it can be considered zero, but it is not actually zero.

>>10127694
The value 1/n can never equal 0, since the 1 is on top.

>>10124605
1/INFINITY = 0
multiply both sides by 2
2/INFINITY = 0
therefore
1/INFINITY = 2/INFINITY
multiply both sides by INFINITY
1 = 2

>>10126474
M-my calculator doesn't get there sir, what do I do?

>>10127699
infinity
An unbounded value that is greater than every real number.

Infinity is not a number.

>>10127908
>multiply both sides by INFINITY
inf/inf is undefined

>>10124609
Define define

>>10126521
>>10127434
Infinity can be a number (as in transfinite ordinals and cardinals, or the Riemann sphere, or the extended real line). It just depends on the context.

>>10128061
>the context.
being a faggot

the rest of us use real numbers

>>10128044
1/INF = 0
therefore
1 = 0 * INF
but
2/INF = 2 * (1/INF) = 0
so
2 = 0 * INF
therefore
2 = 1

>>10128077
>1/INFINITY = 2/INFINITY
>multiply both sides by INFINITY

inf/inf = 2*inf/inf

inf/inf is undefined, cannot continue

>>10126520
Based

which infinity are you using?

>>10128102
>>10128039

>>10128077
you forgot the part where these are only well defined strictly as limits

>>10124605
No, infinity is not a number but rather a concept.
The limit of 1/x however does approach zero as x approaches infinity.
To prove this we need only use l'hopital's rule.
The derivative of the denominator is 1, tge derivative of the numerator is 0
0/1 =1

>>10124605
I like to think that n/infinity infinity stretches n in the x axis (or y, I'm not really well-versed in math).

>>10128531
Infinitely stretches*

>>10128096
inf/inf = inf * (1/inf) = inf * 0 = 1
QED

>>10124605
>Does 1/INFINITY = 0?
This is totally standard. Consider the familiar result
lim x -> inf (1/x) = 0

For this reason, in extended real analysis, we define
1/ inf = 0

>>10124832
Assuming epsilon is a small real number greater than zero, it has a multiplicative inverse. Apply the inverse to both sides gives
1 / (epsilon*infinity)=1

This implies
(epsilon*infinity)=1

There are some contradictions, I think, associated with this last thing.

>>10127434
I find it helpful. In fact, "extended real analysis" was invented for exactly this purpose.

>>10127439
You would have to make a definition for infinitesimally small. Also, it would have to vary as the numerator varies.

>>10127699
Infinity is the endpoint of the positive branch of the extended real number line. All other points on that line are real numbers.

>>10127908
you wrongly assume that infinity has a multiplicative inverse without first demonstrating some number Z such that
infinity (Z) = 1

>>10129388
>inf * 0 = 1
This invokes some contradictions, I forget what they are though.

>>10129433
if in real analysis 1/infinity = 0 then N such that N>0 and N/2 = 0 exists

but this number can't exist.

if you have a sieve whose holes only let things with a diameter of 1 go past. if doesn't matter if you pour an infinite number of things on the sieve, none of them will pass through if their diameters are greater than 1


1/infinity can never = 0 N isn't passed through

>>10129388
inf*0 is undefined brainlet.

>>10129388
undefined= inf * (1/inf) = undefined

>>10129736
It was already assumed that 1/inf = 0
therefore by the definition of division
inf * 0 = 1
Who's the brainlet now?

>>10130445
still, you
inf*0 is undefined

>>10126520

>>10124605
True on the Riemann sphere.

1/0= everything the we do not know

Infinity= everything the we do not know + everything the we know

1/0= infinity- everything the we know

0/1= 1/(infinity- everything the we know)

0= 1/(infinity- everything the we know)

>>10133439
0 = everything this dumb numerology fag knows

Is impossible knows nothing

>>10124605
Have you taken an analysis class?

It’s not a form that has too much meaning without the notion of a limit. When evaluating behavior going to infinity, we generslly show that no matter where we are, we can always get arbitrary closer to a threshold. We say it “equals 0” as a shorthand to say it is effectively 0 with consideration to infinity. This is a very naive, dirty definition as the rabbit hole goes deeper, but it’s a good one to start off of since it tends to the right idea, and you can make corrections to the rigor as you go

>>10129388
Infinity is a concept. The algebra you’re using isn’t well defined for infinity (considering there is in fact an algebra for infinity)