Math

drunkbnu · 2015-12-06 21:04:31

Bimps wrote:

Freckleface wrote:
whats square root of -4?
2i

In this case, negative square roots do not exist unless you use rational terms like an imaginary number that works like a clock if you test it like i^0=1 - i^1=i - i^2=-1 - i^3=-i. The normal ranks are from 0 to 4, trying with higher or lower numbers will work the same like (5|8)=(0|4), meaning that i^5=1

Ratburntro44 · 2015-12-06 21:17:12

Tako wrote:

Why not just use L'Hôspitál?
If you're just trying to evaluate 1/0 you're going to be in a pickle (and I think we've beat that horse into nonexistence) but if instead you have a limit which approaches x/0 or inf/0 or something like that, then you can use L'Hôspitál to reveal the actual answer.
An example:
lim x->0 [sin(x)/x] => 0/0
lim x->0 [sin(x)/x] == lim x->0 [cosx/1] == 1
This also demonstrates why x/0 needs to be undefined. Notice in the first statement I said => 0/0 instead of == 0/0. If I said it equals 0 then I could then say
lim x->0 [sin(x)/x] == 0/0
lim x->0 [2x/x^2] == 0/0
therefore
sin(x)/x == 2x/x^2
1 == 2
which is definitely false.

That's… not an implication that works. You can't say lim x->a [f(x)]=lim x->a [g(x)] implies f(x)=g(x), even at a.

There's also a huge difference between showing why 0/0 needs to be undefined and x/0 needs to be undefined, and since L'Hôspitál's rule only applies to limits of indeterminate forms, which x/0 is not for x \in \mathbb{R} \ {0}.

On the other hand, if you had actually chosen a limit that "approaches" x/0 for x \in \mathbb{R} \ {0} (I use quotation marks because that's not a word that actually makes sense here- limits don't "approach" an expression, they have a value (which the expression the limit is being taken on can be said to approach, but the limit itself doesn't). Moreover, if the expression in the limit did approach, that would require x/0 to have a value, meaning that it would be defined, even though the whole purpose of this is to show why it shouldn't be defined.), then you would probably find the limit to not be defined in the extended real numbers; however, the right and left handed limits would be to positive and negative infinity (not necessarily respectively). This does kind of give a reason for why x/0 shouldn't be defined, but it really has nothing to do with L'Hôspitál's rule.

Stagecrew

Tako · 2015-12-06 21:44:30

There's also a huge difference between showing why 0/0 needs to be undefined and x/0 needs to be undefined, and since L'Hôspitál's rule only applies to limits of indeterminate forms, which x/0 is not for x \in \mathbb{R} \ {0}. On the other hand, if you had actually chosen a limit that "approaches" x/0 for x \in \mathbb{R} \ {0} [...], they have a value [...]. Moreover, if the expression in the limit did approach, that would require x/0 to have a value, meaning that it would be defined, even though the whole purpose of this is to show why it shouldn't be defined.), [...]. This does kind of give a reason for why x/0 shouldn't be defined, but it really has nothing to do with L'Hôspitál's rule.

In my first sentence I said x/0 (for all x != 0) would lead you nowhere but I for some reason forgot about that and started talking about x/0 instead of 0/0. Whoops.

The only reason I went down that rabbit hole is because I remember in my first semester my calculus teacher made a huge deal about never using the expression "= 0/0" because the transitive property of equality would lead you to false conclusions (see example). Time distorted my memory of that "proof" and I hazardously wrote down what I remembered instead of what was true.

So let me revise my example a little bit:
IF
lim x->0 [x^2/2x] = 0/0 AND
lim x->0 [x^2/2x] = lim x->0 [x/2] = 0 (by properties of limits)
THEN
0/0 = 0

BUT IF
lim x->0 [sinx/x] = 0/0 AND
lim x->0 [sinx/x] = lim x->0 [cosx] = 1 (by L'Hôspital's Rule)
THEN
0/0 = 1

THEREFORE
0 = 1

That's the type of example she used, and what I meant to say.

[edit] As one of my high school teachers would say, I deserve to be struck by lightning by the Math Gods.
[edit 2] Wait, you're going to call me out on this but not Riemann's zeta function? I recall someone getting the knickers in a twist last time I posted it here, and there aren't many math enthusiasts.

Ratburntro44 · 2015-12-06 21:56:57

That makes a lot more sense, though it's still potentially possible to define 0/0 without having lim x->0 [x^2/2x] = 0/0. Problem is, lim x->0 [x^2/2x]=0 regardless of whether or not 0/0 is defined; 0/0 being defined wouldn't necessarily imply that the limit can be directly evaluated. Instead, it could just imply that there is a discontinuity in the function at that point. So, while not really proving that having 0/0 defined would be inconsistent, it still does work decently as an example of why it shouldn't be defined.

drunkbnu · 2015-12-06 22:36:36

Actually a way to resolve divisions is that actually, for example, you are told to resolve 20 / 5. It gives 4, but why?
20 / 5 means you have to delete 5 from 20 as many times as you finally reach 0, meaning that 20 / 5 = 20 - 5 = 15 - 5 = 10 - 5 = 5 - 5 = 0
At the end you used 4 times 5 to convert 20 into 0, meaning that the final result is 4, so 20 / 5 = 4

Now what about 20 / 0? In this case, the operation would end like this: 20 - 0 = 20 - 0 = 20 - 0 = 20 - 0 = 20 - 0 = 20 - 0 = 20 - 0 = 20 - 0 = 20 - 0...
And it will never end, meaning that the result is an infinity. I explained my reason of it being undefined at OP.

But what about 0 / 0? In this case, it would end like this: 0 - 0 = 0 - 0 = 0 - 0 = 0 - 0 = 0 - 0 = 0 - 0 = 0 - 0...
But if the actual number is already 0 before we start deleting, that means that there is no such reason to delete value from 0, even if the number you use to delete value from 0 is 0.
So it's a logical reason to say that 0 / 0 = 0. But also remember that 0 / 0 can be converted to 0^0 which also ends in an indeterminate form. The infinity concept is rejected on these cases of 0 / 0 and 0^0. The results can be 0 or 1.

Ratburntro44 · 2015-12-06 23:52:49

Tako wrote:

[edit 2] Wait, you're going to call me out on this but not Riemann's zeta function? I recall someone getting the knickers in a twist last time I posted it here, and there aren't many math enthusiasts.

Yeah, because the way you described it was pretty much accurate, unlike this post, which is the one I believe you are referring to. The only objection I would have as touting it as some "ooh look cool math mysteries". However, looking at is a value assigned from the analytic continuation of Riemann's Zeta function actually gives a legitimate reason for getting that number; you even took care to note that the -1/12 comes from "removing" the infinite part, and not claiming that this type of summation was just the standard and true for every context. It's quite better than giving unexplained bad proofs and conflating different types of summation (and treating one as if it were the "correct" type).

Tako · 2015-12-07 08:02:56

Ratburntro44 wrote:

Yeah, because the way you described it was pretty much accurate, unlike this post, which is the one I believe you are referring to..

Yeah for that topic I was relying on the words of a Youtube video. The speaker was a science professor of sorts but nonetheless it's a layman's "proof".

Bimps · 2015-12-07 21:42:36

2+2=4 amirite guys???? lol i am such a #nerd

Ratburntro44

!nb4 · 2015-12-08 06:59:45

but seriously, I just learned - and + today.
something like (45) - (-78)
pretty sure its 123

so basicly (-1) x (-78) = +78
um then +45 +78= +123

Anch · 2015-12-08 21:40:04

AYB wrote:

but seriously, I just learned - and + today.

When I first read that I thought you meant you just learned addition and subtraction, but then I realized you meant using operations on negative numbers.

KingFudge, Zumza

Bimps · 2015-12-08 22:34:17

what the **** is a math srs pls help im gonna fail my math test tomorrow what is 2+2

Badoosh, Ratburntro44

Anch · 2015-12-08 23:10:51

Bimps wrote:

what the **** is a math srs pls help im gonna fail my math test tomorrow what is 2+2

Bimps wrote:

2+2=4 amirite guys???? lol i am such a #nerd

Badoosh, Stagecrew, Pingohits, Onjit, Bobithan

Gosha · 2015-12-09 21:17:11

New thing:

Imagine a square, what you cut in halfs
Something like this:

and you cut it, cut it and cut it
so, will you ever end? no. becasue it is ininity number or cuts.
It means what we cant cut this square for infinity times right? Wrong.

Lets do this: cut 1st piece in 30 seconds
2nd piece in 15 seconds
3rd piece in 7.5 seconds
4th in 3.75 seconds
and so on.
yea, you need to cut 20th piece for 0.00005722045.. seconds, but lets doesnt count your physical possibilites and lets say you can do it
so, what would happend in 1 minute? you'll cut "all" pieces?

Processor · 2015-12-09 21:28:04

Easy,

Yes after one minute you finish cutting.

Onjit, Ratburntro44

Terrasher · 2015-12-09 21:28:34

Goshanoob wrote:

New thing:
Imagine a square, what you cut in halfs
Something like this:
http://i.imgur.com/6GcClGS.png
and you cut it, cut it and cut it
so, will you ever end? no. becasue it is ininity number or cuts.
It means what we cant cut this square for infinity times right? Wrong.
Lets do this: cut 1st piece in 30 seconds
2nd piece in 15 seconds
3rd piece in 7.5 seconds
4th in 3.75 seconds
and so on.
yea, you need to cut 20th piece for 0.00005722045.. seconds, but lets doesnt count your physical possibilites and lets say you can do it
so, what would happend in 1 minute? you'll cut "all" pieces?

I see someone has watched Vsauce's latest video.

Tako, Onjit

KingFudge · 2015-12-09 21:42:18

What about that thing on Numberphile on glitch numbers?I think it was 10^506-10^203-1 is a prime number. Was kinda cool.

drunkbnu · 2015-12-09 23:03:53

Goshanoob wrote:

New thing:
Imagine a square, what you cut in halfs
Something like this:
http://i.imgur.com/6GcClGS.png
and you cut it, cut it and cut it
so, will you ever end? no. becasue it is ininity number or cuts.
It means what we cant cut this square for infinity times right? Wrong.
Lets do this: cut 1st piece in 30 seconds
2nd piece in 15 seconds
3rd piece in 7.5 seconds
4th in 3.75 seconds
and so on.
yea, you need to cut 20th piece for 0.00005722045.. seconds, but lets doesnt count your physical possibilites and lets say you can do it
so, what would happend in 1 minute? you'll cut "all" pieces?

That's exactly why dividing by 0 is undefined. You would keep cutting pieces and there you would never end until you reach the minute. If the result is gotten someway it will be an infinity. It's really something surprising.

Ratburntro44 · 2015-12-10 00:09:05

Goshanoob wrote:

New thing:
Imagine a square, what you cut in halfs
Something like this:
http://i.imgur.com/6GcClGS.png
and you cut it, cut it and cut it
so, will you ever end? no. becasue it is ininity number or cuts.
It means what we cant cut this square for infinity times right? Wrong.
Lets do this: cut 1st piece in 30 seconds
2nd piece in 15 seconds
3rd piece in 7.5 seconds
4th in 3.75 seconds
and so on.
yea, you need to cut 20th piece for 0.00005722045.. seconds, but lets doesnt count your physical possibilites and lets say you can do it
so, what would happend in 1 minute? you'll cut "all" pieces?

Judging by your picture, all of the cuts correspond to cutting an existing piece in half (vertically)
If we then identify the original square with the interval from 0 to 1, each cut corresponds to a multiple of a (negative) power of 2.
Even if we are considering possible cuts only to be rational numbers, this leaves an infinite number of possible cuts that are never made.
However, if we consider the possible cuts to be all real numbers (on the interval), then not only is that true, but almost all of the possible cuts will never be made.

So, it depends how exactly you define cutting "all" pieces note this is just me making an overly extended dumb joke not trying to claim that limits aren't real or something stupid like that

Tako · 2015-12-10 21:48:33

HG wrote:

Goshanoob wrote:
yea, you need to cut 20th piece for 0.00005722045.. seconds, but lets doesnt count your physical possibilites and lets say you can do it
so, what would happend in 1 minute? you'll cut "all" pieces?
That's exactly why dividing by 0 is undefined. You would keep cutting pieces and there you would never end until you reach the minute. If the result is gotten someway it will be an infinity. It's really something surprising.

This has nothing to do with dividing by 0? You're dividing the square and the time it takes to cut that square by 2, not 0. 0 doesn't even exist in this problem.

Kamekthemagician · 2015-12-10 21:59:43

a/b = x --> x · b = a

1/0 = Impossible --> Can you find any number that complies this: x · 0 = 1? No... Every number · 0 is 0...

0/0 = Undefined --> Can you find any number that complies this: x · 0 = 0? Yes... All the numbers you can think.

Tako · 2015-12-10 22:26:22

Kamekthemagician wrote:

a/b = x --> x · b = a
1/0 = Impossible --> Can you find any number that complies this: x · 0 = 1? No... Every number · 0 is 0...
0/0 = Undefined --> Can you find any number that complies this: x · 0 = 0? Yes... All the numbers you can think.

That's a very elegant way to put it.

Gosha · 2015-12-11 14:07:54

Terrasher wrote:

Goshanoob wrote:
New thing:
Imagine a square, what you cut in halfs
Something like this:
http://i.imgur.com/6GcClGS.png
and you cut it, cut it and cut it
so, will you ever end? no. becasue it is ininity number or cuts.
It means what we cant cut this square for infinity times right? Wrong.
Lets do this: cut 1st piece in 30 seconds
2nd piece in 15 seconds
3rd piece in 7.5 seconds
4th in 3.75 seconds
and so on.
yea, you need to cut 20th piece for 0.00005722045.. seconds, but lets doesnt count your physical possibilites and lets say you can do it
so, what would happend in 1 minute? you'll cut "all" pieces?
I see someone has watched Vsauce's latest video.

Kek

Tako · 2015-12-11 19:04:23

Is there a mathematical way to wrap presents using only one sheet of paper?

I have a solid that has a square top, a square bottom, and trapezoidal sides.

Maybe if I put the largest square on a sheet of square paper, then fold each side up ignoring the excess, then I can fold the excess over to the side. OR... I can fold the excess as I'm folding up the sides so it looks neater. The last corner will be hard, though, because it'll have to go inside something that's already folded.

I think this is just origami, not math.

What about a frying pan? Lol.

Anch · 2015-12-11 21:47:22

Tako wrote:

Is there a mathematical way to wrap presents using only one sheet of paper?

You can wrap presents using only one sheet of paper by solving this expression: 1 + 1

Bimps · 2015-12-11 22:50:22

srs what is 2+2

Ratburntro44

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#26 2015-12-06 21:04:31, last edited by drunkbnu (2015-12-06 21:05:17)

Re: Math

#27 2015-12-06 21:17:12, last edited by Ratburntro44 (2015-12-06 21:17:33)

Re: Math

#28 2015-12-06 21:44:30, last edited by Tako (2015-12-06 21:58:27)

Re: Math

#29 2015-12-06 21:56:57

Re: Math

#30 2015-12-06 22:36:36, last edited by drunkbnu (2015-12-06 22:57:19)

Re: Math

#31 2015-12-06 23:52:49

Re: Math

#32 2015-12-07 08:02:56

Re: Math

#33 2015-12-07 21:42:36

Re: Math

#34 2015-12-08 06:59:45, last edited by !nb4 (2015-12-08 07:01:24)

Re: Math

#35 2015-12-08 21:40:04

Re: Math

#36 2015-12-08 22:34:17

Re: Math

#37 2015-12-08 23:10:51

Re: Math

#38 2015-12-09 21:17:11

Re: Math

#39 2015-12-09 21:28:04

Re: Math

#40 2015-12-09 21:28:34

Re: Math

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Re: Math

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Re: Math

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Re: Math

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Re: Math

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Re: Math

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