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/sci/ - Science & Math

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Why is this so controversial?
You can pretend that $\sqrt{-1}$ exists so why can't you pretend that this does too?
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You can, it's just less useful than i
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>>12925408
You can, I think the algebra is called a wheel. I haven't looked into it much.
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>>12925408
you can, but it's useless
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>>12925408
ok, but how do you differentiate it from 2/0?
And then, how do you relate both of them to 0/1 and 0/2?
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>>12925431
1/0 = infinity
2/0 = two infinities
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>>12925425
>>12925418
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>>12925408
I get $0 an hour because I have no job How long until my job earns me$1

You see the problem.
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>>12925536
Based and infinite pilled
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>>12925583
shit tier analogy.

Why do you fags have a problem with the fact that division by zero is simply undefined?
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>>12925583
I get $$i$ an hour because I have no job How long until my job earns me$1
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>>12925626
-i, you need to go to before you started imagining things and get a real job
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>>12925583
Valid analogy
>>12925626
Invalid analogy, there's no job that pays i, unlike jobs that pay 0 i.e. no job.
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>>12925708
>Invalid analogy, there's no job that pays i, unlike jobs that pay 0 i.e. no job.
False. There are no jobs that pay 0. You cannot be paid 0 and when you work for free you are not paid 0, you're simply not paid - the process of payment is not there.
It's a false semantic perversion that does not actually exist in reality, it's not a quantity.
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>>12925717
>You cannot be paid 0 and when you work for free you are not paid 0, you're simply not paid
You sound like people who say "zero is not a number"
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>>12925583
in this case the answer would be infinite time?
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>>12925583
I hav one potato
i splet pot to in zero bices
how many poato i hae?
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>>12925770
More like how big is each piece.
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>>12925560
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>>12925408
It's because introducing 1/0 breaks ring properties.
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>>12925408
We do, we just call it "undefined"
Also i doesnt "exist" in the reals, or the integers, etc etc, its not about "existing," its about a useful construct. 1/0 is useful in calculus, because we can say it is undefined, and hence slope of 1/0 is undefined. Even more useful than 1/0 is 0/0, an indeterminate form, because this enables to use lhospitals rule on a limit.

Do you think mathematicians just see 1/0, throw up their hands, and go "well see we just cant have this"?
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>>12925858
>but the axioms!!!!!!!
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>>12925408
i is more of a number. 1/0 is more of a tool. Real mathematicians know the difference.
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>>12925536
>2/0 = two infinities
and beyond
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>>12925920
>x/0 = x infinities
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>>12925408
Because division is not applicable to nothing. To pretend it is, is to equate every possible divisor with one another (i.e. 69=420), as every "nullth" represents the same value.
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>>12925879
This but unironically
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>>12925431
>how do you relate both of them to 0/1 and 0/2?
should be irreducible, desu
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>>12925583
you get 1 dollar for every hour you dont work, hence you get infinite money
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>>12925896
Best summary, basically what i meant by >>12925867
Thanks anon
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Am I incorrect?
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>>12925751
Retard. The longer he works his total earnings does not get closer to $1. >> >>12925583 Well, your "job" could be walking to the store, and on your way you find$1 laying on the street.

Your job just earned you $1 >> 1/0 = infinity >> >>12926105 that's the limit which is different. the limit to inf of 1+x is inf but saying 1+inf means "what is bigger than infinity by one". limits are like the upper limit or the value that the variable never crosses >> A math undergrad here. In linear algebra it isn't defined in any structure (G,$,#) that has two operations, both of which are groups in respect to set G, simply because 0 isn't invertible in a field. Let say that it has an inverse, 0 is defined so that 0$n=n and the$ resembles addition(it doesn't have to be addition per se). It is easily proven by the axioms that for any given object in set G x#0=0, where # resembles multiplication(it doesn't have to be). Now from distributivity we get that x$x#0=x#(e+0)=x#e=x (*)where e is some kind of no. one. Now, we said earlier thay 0 has a multiplicative invers, that means that a#0=e for some a in G. But from the (*) we conclude that any element of G #0 must be 0, because there is only one such element(@). Therefore, we get that 0=e which is a contradiction and that proves that 0 doesn't have a multiplicative invers. @ is really easy to prove, lets suppose that there are two 0 such that n$0=n and we'll call them 01 and 02. Since we now that both neutral elements for $(01,02) fulfill those properties, we get that 01=01+02=02+01=02 that is there is onle one neutral for$. And that's the whole proof that zero doesn't have an inverse for multiplication. (inverse for multiplication is actually the element you divide with, there isn't actually such thing as division defined in linear algebra at least).
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Also, i is not the square root of -1, i2=-1 and there are some big differences betweem those two statements, complex numbers are actually structures that are given by a twople (x,y) with * and + defined very differently than * and + in the field of real numbers, you cannot compare those two, that's just silly.
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>>12925408

One of them leads to contradictions and the other one doesn't, that's the difference.
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>>12925924
>infinite/0 = infinite infinities
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>>12925431
How can one differentiate 1*0 from 2*0?
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a*b=c
solve for a when b=0 and c=1
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>>12925408
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>>12927490
a=inf
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another episode of anon learns what calculus and infinitesimals are
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>>12929345
Are you braindead, there is a distinction, it is still 0 and not a limit.
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>>12925751
Not even infinite time will get him closer to \$1.
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>>12925408
> controversial

you mean we should... teach the controversy?
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>>12925920
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The only reason i care about this is baseball. If a pitcher allows an earned run but doesn't record an out and is then removed, his earned run average for the game is infinite. This happens at the start of every season to a pitcher or two. Undefined is a shitty way to describe this phenomena. That pitcher over the course of 9 innings pitched, statistically, would allow infinite runs since he would never record an out. That isn't undefined.
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If you want it defined like i just do the same thing

1/0 = p
2/0 = 2p

Where p is a new constant introduced. Don’t know how useful it is though
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>>12925408
I am Wildburger, and I can confirm that I approve.
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>>12925408
How would you fit something into nothing? Basically the same logic.
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>>12925536
>infinity
that would be an attempt to evaluate the expression, which you shouldn't, just like you don't evaluate the root of negative numbers
you should take the long route instead and have it stick out as a tumor in your equation until you can eventually cancel it out
something like this:

$\frac{1}{0} = N$
Multiplication:
$xN * 0 = x$
Division:
$\frac{x}{N} = x\frac{0}{1} = 0$
Exponentiation:
$N^x = \frac{1^x}{0} = N$ for $x > 0$
$N^x = \frac{0}{N^x} = 0$ for $x < 0$
$N^0 = \frac{1}{0} = N^{1}N^{-1} = N$
In fact the above gives a multiplicative inverse:
$N^{1}N^{-1} = \frac{N}{N} = 1$

So you see, you don't have to worry about infinities and undefined behavior if you just pretend that it's not there until it eventually gets canceled out by a multiplication by 0 and outputs its numerator as a real number.
The problem is here:
$2 * \frac{1}{0} * 0$
Do we get a $(2 * \frac{1}{0}) * 0 = 2N * 0 = 2$, or do we get a $(2 * 0) * \frac{1}{0} = 0 * N = 1$
But worry not because even the standard algebra does not have a valid order of operations. It pretends that it does, but similarly, it must impose conventions to avoid this >>12900569
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>>12925920
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>>12933817
wait my bad the $N^0$ line is actually
$N^0 = N^1 N^{-1} = \frac{1}{0} * 0 = 1$
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>>12925920
joke of the year, kekk
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>>12925408
it's equal to infinity. End of story
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>>12925408
>pretend
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>>12925536
Based retard.
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>>12933705
How would you square something but get a negative number?
Doesn't make sense, b/c -*-=+.
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>>12927507
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Look up Alexandroff compactification of the real number line. Look up projective geometry.
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>>12925717

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>>12925867
Lhopitals rule is for braindead idiots who cant just plug in numbers almost equivalent to what the limit is heading to.
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>>12935539
>a=b
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>>12925408
If it were to be defined as anything, then 1 would equal 0 by definition (multiply both sides by 0). Which doesn't make any sense. Hence it is undefined, not just infinity as some people in this thread wrongly think, but literally a non-object because if it were to be one then numbers wouldn't work
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>>12925609
>Why do you fags have a problem with the fact that division by zero is simply undefined?
It's not defined as a function from reals to reals, but there's no reason you can't define division as a binary operation over a set of numbers that includes zero.
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>>12925408
>Why is this so controversial
It isn't. It doesn't exist and virtually nobody (except you, faggot) disputes that.
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Hitomi's number.
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>>12925609
Because infinity isn't usually a defined element...
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>>12925408
Back to >>12940872 faggot
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Dammit! You broke mathematics!
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>>12925408
>why can't you pretend that this does too?
If you define an output for this operation, it is easy to show the operation is not well defined.
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>>12943196
what region are you from? you write your t sort of like we write z.
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>>12943254
'Merica! Yourself?

This isn't common in the United States. I'm learning Italic handwriting during quarantine. Have to do something to pass the time
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>>12943305
me too, yeah i’d never seen that before, i thought it was maybe a regional thing or european or something. cool

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