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Re: Concept of "infinity"

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1waffle1 is not online. 1waffle1
Joined: 16 Oct 2007
Total Posts: 16381
22 Aug 2011 12:25 AM
Okay, I'm just looking at this from my point of view.

Relative to the decimal system, as if "infinity" was a number, it would be bigger than any other number other than itsself, or another conceptual number that overrules it.

If you take away infinity from infinity, it's zero. that's it. it isn't undefined, it's zero. Why would it be undefined? You have a number, and take THAT NUMBER away from THAT NUMBER, there is NOTHING left. ZERO. [/rage]

if you subtract an actual number from infinity, it's still infinity.

MORE INFINITY. There aren't as many numbers between 1 and 2 as there are between 1 and 3. TRUTH. Even though we know it's BOTH INFINITY, there is still MORE between one and three. It's OBVIOUS.

There are infinite points on a line. There are infinately more points for every point on that line in a plane. Even though it's both INFINITY, which apparently HAS TO BE THE SAME, ALWAYS, logically, it ISN'T TRUE. If you did ANY OF THIS MATH with a number that wasn't so FAKE, it would MAKE COMPLETE SENSE. [/rage]

Anyone else who thinks differently about it, to me, is stupid. No matter how you try to explain it, there is no way I can find your logic to be logical any more than mine.
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MajorTAntiSec is not online. MajorTAntiSec
Joined: 19 Aug 2011
Total Posts: 81
22 Aug 2011 12:31 AM
Yea, but that means nerd-raging about it won't be as fun.

So STFU
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Tenal is not online. Tenal
Joined: 15 May 2011
Total Posts: 18684
22 Aug 2011 12:31 AM
[ Content Deleted ]
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Fungalmungal is not online. Fungalmungal
Joined: 18 Oct 2008
Total Posts: 2519
22 Aug 2011 12:51 AM
"If you take away infinity from infinity, it's zero. that's it. it isn't undefined, it's zero"

It's undefined because infinity has no fixed "size". One infinity could be "larger" than the other.

Infinity + 1 = Infinity -- >
Infinity + 1 - Infinity = Infinity - Infinity --?
1 = Infinity - Infinity
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Patacorow is not online. Patacorow
Joined: 29 Dec 2007
Total Posts: 1359
22 Aug 2011 01:12 AM
Fungal, everything you said is right except for

1 = Infinity - Infinity

since

Infinity - Infinity = 0

therefore this is obsolete;

1 = 0
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JulienDethurens is not online. JulienDethurens
Joined: 11 Jun 2009
Total Posts: 11046
22 Aug 2011 01:22 AM
"
If you take away infinity from infinity, it's zero. that's it. it isn't undefined, it's zero. Why would it be undefined? You have a number, and take THAT NUMBER away from THAT NUMBER, there is NOTHING left. ZERO. [/rage]"

Lolnope.

Infinity + Infinity = Infinity, so I guess it'd be logical that Infinity - Infinity = Infinity.

Infinity + Infinity = infinity. How couldn't Infinity - Infinity equal Infinity? That'd make no sense.
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JulienDethurens is not online. JulienDethurens
Joined: 11 Jun 2009
Total Posts: 11046
22 Aug 2011 01:25 AM
Infinity has no precise size. One infinity could be larger than another. They are infinite, not finite. They are undefined. Infinity - Infinity = Infinity, all of that knowing that all of these infinity might have different sizes. And there is no way to calculate it, that is precisely why they are considered as 'undefined'.
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Prehistoricman is not online. Prehistoricman
Joined: 20 Sep 2008
Total Posts: 12490
22 Aug 2011 03:15 AM
So? Even if they are undefined, inf - inf = 0.

x - x = 0 ALWAYS

x to the power of 0 = 1 ALWAYS

x is undefined. Does that makes these statements false?
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pighead10 is not online. pighead10
Joined: 03 May 2009
Total Posts: 10341
22 Aug 2011 03:40 AM
Okay, pupils! Let's count 100 places, starting from the highest number possible!

"infinity
infinity and one
infinity and two
infinity and three
infinity and four
infinity and five
infinity and six
infinity and seven
..."
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pighead10 is not online. pighead10
Joined: 03 May 2009
Total Posts: 10341
22 Aug 2011 03:46 AM
um back on topic

Let's say infinity is x.

x - x = 0

Infinity is undefined, therefore so is x, but x - x still equals zero. If you're arguing that one infinity could be larger than another, then you can't put it into an equation like that anyway, and you're right. But then you're saying

infinity - infinity = infinity
==
a - b = c

which it doesn't.
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JulienDethurens is not online. JulienDethurens
Joined: 11 Jun 2009
Total Posts: 11046
22 Aug 2011 03:56 AM
"So? Even if they are undefined, inf - inf = 0.

x - x = 0 ALWAYS

x to the power of 0 = 1 ALWAYS

x is undefined. Does that makes these statements false?"

You're perfectly right.

The thing is, infinity != infinity. Yeah, that's right. Infinity isn't equal to infinity.

x - x = 0. Yep. Except in this case, it's the same value, AKA : x. If you calculate infinity - infinity, it ISN'T the same value. Yep, that's why infinity is undefined. An infinity could be larger than another.

Infinity + 1 = infinity. The second infinity is larger than the first. If you put them in variables such as x, that'd make no sense, since x wouldn't be equal to x. Yes, if x = infinity, x - x = 0. But it doesn't mean that infinity - infinity = 0, since actually, both infinitys AREN'T NECESSARILY IDENTICAL, meaning the result of the calcul could be ANYTHING, which is precisely why we say it is undefined (or infinity, actually, since it's pretty much the same).

Happy?
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JulienDethurens is not online. JulienDethurens
Joined: 11 Jun 2009
Total Posts: 11046
22 Aug 2011 04:04 AM
Also, nope, inf ^ 0 != 1.

Exponents are just multiplications, which are just additions. Since infinity + infinity = undefined (or infinity, if you prefer), it directly means that any calcul using multiplications, divisions or exponentiations will NECESSARILY end up in undefined.

Inf + inf = inf.
Inf * inf = inf.
Inf / inf = inf.
Inf ^ 2 = inf.
Inf ^ 1 = (inf ^ 2) / inf = inf / inf = inf.
Inf ^ 0 = (inf ^ 1) / inf = inf / inf = inf. YEP! EXACTLY. Inf ^ 0 = 1.

For those that didn't know, there's a reason that any number that is not undefined ^ 0 = 1. It's not just random. Think about it this way:

2 ^ 2 = 4.
2 ^ 1 = 2, which is actualy (2 ^ 2) / 2.
Meaning that 2 ^ 0 = (2 ^ 1) / 2, which actually results in 1. But if you apply the same logic with infinity, it DOESN'T give you 1, since inf / inf != 1.

The only reason that a number ^ 0 would be equal to 1 is that that same number divised by itself would equal 1, WHICH IS NOT THE CASE FOR INFINITY.
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sdfgw is not online. sdfgw
Top 50 Poster
Joined: 08 Jan 2009
Total Posts: 41681
22 Aug 2011 07:54 AM
i received a PM about this thread

unfortunately my incredible and indisputable knowledge of everything ('cept matrices) extends to infinity in such ways it would make your head explode in infinite pieces, each piece the size of your head / infinity (or if you're being pedantic, 1/infinity which = 0, so the pieces would deatomise and essentially disintegrate)

where was i

oh yeah

"Even though it's both INFINITY, which apparently HAS TO BE THE SAME, ALWAYS, logically, it ISN'T TRUE. If you did ANY OF THIS MATH with a number that wasn't so FAKE, it would MAKE COMPLETE SENSE."

i vote we leave it there
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Aaaboy97 is not online. Aaaboy97
Joined: 05 Apr 2009
Total Posts: 6612
22 Aug 2011 08:03 AM
"x to the power of 0 = 1 ALWAYS"

0^0 = undefined

trololololololololololololololololololololol
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sdfgw is not online. sdfgw
Top 50 Poster
Joined: 08 Jan 2009
Total Posts: 41681
22 Aug 2011 08:10 AM
x^0 = x / x

that's basically where x^0 = 1 comes from

so x^0 = 0 / 0 = UH OH
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JulienDethurens is not online. JulienDethurens
Joined: 11 Jun 2009
Total Posts: 11046
22 Aug 2011 08:15 AM
"so x^0 = 0 / 0 = UH OH"

Nope, that's true only if x = 0.

Also, infinity ^ 0 != 1. Why? Because infinity / infinity != 1. =)
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sdfgw is not online. sdfgw
Top 50 Poster
Joined: 08 Jan 2009
Total Posts: 41681
22 Aug 2011 08:19 AM
sorrehs, that's what I meant. 0^0 *

Okay then. Here's a Q. What's infinity^-1?
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JulienDethurens is not online. JulienDethurens
Joined: 11 Jun 2009
Total Posts: 11046
22 Aug 2011 08:24 AM
infinity^-1 = undefined.

Actually, whatever operation you use on infinity, it'll always give you undefined. =)

That includes inf / inf, inf * 0, inf ^ 0 and inf - inf.
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sdfgw is not online. sdfgw
Top 50 Poster
Joined: 08 Jan 2009
Total Posts: 41681
22 Aug 2011 08:27 AM
x ^ -1 = 1/x?

Seems plausible to me.
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JulienDethurens is not online. JulienDethurens
Joined: 11 Jun 2009
Total Posts: 11046
22 Aug 2011 08:31 AM
owait... You're right.

I failed.

infinity ^ -1 = 0. =/

I failed. Too tired, I guess. ;o
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Danster5oo is not online. Danster5oo
Joined: 27 Aug 2010
Total Posts: 10003
22 Aug 2011 08:36 AM
My brain hurts

-Beardo
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Infinitive is not online. Infinitive
Joined: 21 Apr 2010
Total Posts: 2619
22 Aug 2011 08:46 AM
im infinity
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Danster5oo is not online. Danster5oo
Joined: 27 Aug 2010
Total Posts: 10003
22 Aug 2011 09:01 AM
Infinitive < Infinity
true

-Beardo
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sdfgw is not online. sdfgw
Top 50 Poster
Joined: 08 Jan 2009
Total Posts: 41681
22 Aug 2011 09:06 AM
So I suppose we could draw:


infinity ^ x =

infinity if x > 0
0 if x < 0
undefined if x = 0

hm?
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pighead10 is not online. pighead10
Joined: 03 May 2009
Total Posts: 10341
22 Aug 2011 09:08 AM
x is undefined

infinity is undefined

x - x = 0

infinity - infinity = 0

Unless infinity doesn't equal infinity

which means you're saying:

infinity - infinity = infinity
==
a - b = c

WHICH BREAKS TEH RULES OF ALGEBRA

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