Proof

[Reach]

Originally Posted by spyke252

I thought saying .9 repeating was understood to mean
_
.9, which is a decimal with an infinite number of nines behind it. It seems like common sense to me, as you can't measure how fast a nine is behind a decimal.

It seems easier to just say 1.

But yea, I suppose if by repeating you are assuming the repetition exists infinitely, then it's correct, for sure.

I just remember losing points on a test once for writing a repeating decimal like that instead of the fractional value...XD



Infinity isn't a number, but it's certainly a concept. And conceptually, if there are an infinite number of 9's behind a decimal than you have one. It's kind of hard to imagine because nothing that represents infinity actually exists.

For example, if you were to try to imagine an infinite velocity you would start getting quite confused. Imagine that. It would require an infinite acceleration. How would you even go about moving in that case? Would you not move or simply exist everywhere that exists all at once? ;o (or well, for the sake of calculus you can just write DNE ^_^).



The same goes for trying to say you have 'infinite something' . It would be impossible to prove there is infinite anything because it exists everywhere that can exist at any given time, therefore it would be impossible to ever prove it true as finite beings.

And then you have the paradox of something infinitely small not existing at all.

anyway

[WillTalbot]

Originally Posted by Cavernio

What makes something proveable? Is seeing believing? Is feeling believing? Is mathematically proving something mean you believe its true, its factual?

Once again, try the dictionary ... ugh I'm sick of saying it already.

[Afrobean]

Originally Posted by Reach

It's kind of hard to imagine because nothing that represents infinity actually exists.

Sideways 8s don't exist.

Also, klein bottles and mobius strips also don't exist.



I believe that it only becomes hard to imagine the concept of infinity when you try to imagine it as a numerical value.

[WillTalbot]

for all we know the universe could be infinite, we can't prove it is or that it isn't.

[Reach]

Sideways 8s don't exist.

Also, klein bottles and mobius strips also don't exist.



I believe that it only becomes hard to imagine the concept of infinity when you try to imagine it as a numerical value.

Representing infinity as in, the concept, not the symbol for it. >.>

You can certainly imagine what infinity is like, but it is tough.

for all we know the universe could be infinite, we can't prove it is or that it isn't.

It's quite easy to prove the visible universe is finite.

- The universe is expanding at a given rate.
- Therefore, the universe is finite.

Simple, isn't it?

[WillTalbot]

Infinite is something that goes on forever. Since the Universe is constantly increasing, wouldn't that make the universe infinite? Your probably right but for some reason I can't understand the meaning of infinity as well as I understand most of the other things discussed in CT

[Reach]

Originally Posted by WillTalbot

Infinite is something that goes on forever.

Here's where you're going wrong on the infinity concept.

'Goes on' is incorrect.

Infinity cannot increase or decrease. Something that can increase or decrease is bounded. Anything, by definition that is bounded by something is not infinite.


In this case the universe is bounded by it's rate of expansion. Unless the rate of expansion was infinite, it cannot be infinite (and an infinite expansion rate would mean it exists everywhere at once >.>).



To make it something really easy to grasp, imagine blowing up a balloon. No matter how long, how hard you blow into the balloon (assuming it doesn't pop XD), you can always measure the amount of space inside the balloon as a finite number.


I can see a little kid now that keeps on writing numbers and then asks his mommy 'am I at infinity yet!!??'.

[WillTalbot]

I get it now, I thought infinite was constantly increasing.

[Kilgamayan]

I wish I remembered the limit proof that .9~ = 1.

The only one I ever bother to remember is asking to solve for x in the inequality .9~ < x < 1. >_>

[spyke252]

Hmmm, I got to thinking a few minutes ago. Tell me if anything is wrong with this statement. (Please understand the concept of different bases)

.F repeating (Base 16) = 1, for the same reasons as mentioned earlier. 15 * (1/16^1 + 1/16^2+.... + 1/16^n)
.1 repeating (Base 2) = 1. (1/2 + 1/4 + ... + 1/2^n)

F base 16 = 1111 base 2.

so, would it follow that:

1111 (base 2) * {1/16^n} = {1/2^n} (Both = 1)
1/16^n = 1/2^n * 1/8^n
1111 (base 2) = 15
15 * {1/8^n} = 1 (Dividing both sides by the series {1/2^n})

However, 7 * {1/8^n} = 1 as well.

I'm tired, so I probably made a mistake somewhere. Otherwise, I broke Math, as 15/7 = 1.

[WillTalbot]

Is that calc or something? I definitly did not learn that yet. Somehow I understood it though.

[spyke252]

It's a mixture of calc and CS. Though, maybe you learn about different bases in math somewhere...

[WillTalbot]

I take Algebra, I'm actually a year ahead. Pre-algebra and 8th grade math are more common with 8th graders.

[Afrobean]

Haha.

In 8th grade algebra and they think they can understand calculus.

As for what's going on there: are you doing math with binary and hexadecimal or what? That would be dumb.

[spyke252]

Originally Posted by Afrobean

As for what's going on there: are you doing math with binary and hexadecimal or what? That would be dumb.

Please explain.

[WillTalbot]

Originally Posted by Afrobean

Haha.

In 8th grade algebra and they think they can understand calculus.

As for what's going on there: are you doing math with binary and hexadecimal or what? That would be dumb.

Yeah I know it's pretty hard, I actualy read calc lessons online its confusing as heck! Some of the more simple problems i got though

[spyke252]

Nevermind. I sat down with a math major from another forum I frequent and found the mistake: You can't multiply the two summations of the series to get the other series.

EDIT: Nothing to do with my bases problem, afro.

[this_n00b_rocks]

I'm not sure if anyone posted this, but it's a lot easier to disprove something, and really hard to prove it.

2+2=4
DISprove it.

[Afrobean]

For the same reason that it's impossible to objectively prove something, it's also impossible to objectively disprove something.

[studmuffin51306]

Originally Posted by this_n00b_rocks

I'm not sure if anyone posted this, but it's a lot easier to disprove something, and really hard to prove it.

2+2=4
DISprove it.

2 = 1.5
3 = 3
4 = 4
2+2 = 3

the only reason why you wouldn't disprove it is because assigning numbers different values goes outside of what is generally accepted in math.

Originally Posted by Reach

To make it something really easy to grasp, imagine blowing up a balloon. No matter how long, how hard you blow into the balloon (assuming it doesn't pop XD), you can always measure the amount of space inside the balloon as a finite number.

True, if you can define our universe as a seperate thing from space itself, then yes, it is finite. But the fact is, we haven't seen other universes, so as far as we know, it could stretch as far as space itself. So then you get into the "so what's beyond that?" argument.