Is the Universe Infinite?

#201

You don’t know anything about math, do you? :3

You would be surprised to see how much knowledge in math is completely without any purpose nor any application in the real universe.

Yeah, yeah, and e=1. :facepalm:

There was an engineering professor that published an article saying e=1. He said he calculated (1 + 1/x)^x for a big number of x and his hand calculator gave the result 1. That dumbass used a machine without even taking into account the errors of approximation :facepalm: Well, that was a good laugh for me and my colleagues. The best joke of the year :slight_smile:

According to that WikiAnswers’ link you provided, Yasumasa Kanada and his team said they found “all” digits of pi. They never stated that, they just set a new world record of number of digits in pi that were already calculated. He found 1,241,100,000,000 decimal places. The current world record, according to wikipedia, is 2,699,999,990,000 decimal places. And, let’s face it, Wikipedia > > > WikiAnswers.

No, no, sir, pi does not end because it is irrational, but also transcendental, which means it is not a root of any polynomial with integer coefficients. If someone proved pi does have an end, mathematics would fall apart. The entire basis of math would be compromised, every result already obtained would not be trustable. But, don’t worry, that didn’t happen yet, math is still firm and solid :slight_smile:

Oh, and by the way, pi does have an “infinite” property of some sort. Choose any sequence of decimal digits (finite, but as large as you wish). Anything you want. You will find that exact sequence somewhere in the decimal expansion of pi.

#202

Well, that’s actually interesting. Has it been proven? So for example, is there somewhere a sequence “111111111111111111111111111111111111111” ? That would be the case if the sequence was totally random, but is it proven that it’s random and there is no pattern at all?

EDIT: Actually it’s hard to find a reason why there would be any pattern, but anyway, the question still remains.

#203

Yes. That sequence will appear. Pi is infinite so it is impossible for it to not appear, because with infinite digits there’s infinite chance for every sequence you could imagine.
Or something like that.

#204

i admited pie being infinite was a bad example and a poor example in relation to what I was trying to get at (If any relation at all :S)

"By our third year, most of us will have learned to count. Once we know how, it seems as if there would be nothing to stop us counting forever. But, while infinity might seem like an perfectly innocent idea, keep counting and you enter a paradoxical world where nothing is as it seems.

Mathematicians have discovered there are infinitely many infinities, each one infinitely bigger than the last. And if the universe goes on forever, the consequences are even more bizarre. In an infinite universe, there are infinitely many copies of the Earth and infinitely many copies of you. Older than time, bigger than the universe and stranger than fiction. This is the story of infinity"

Synopsis of the show I watched, massive mind melter. Curse you infinty and my tiny human brain lol

#205

Theoretically, if the number if infinitely long there is no way the sequence could indefinitely never appear.

#206

A sequence of 1/7 digits is also infinite but there is no every possible combination. This is of course a rational number and a different story… Anyway, that was a stupid question, forget that I asked.

#207

Yes, it has been proven! Not only in base ten, but, iirc, in any base. And pi does not have a pattern except for the (various) formulas that generate it. It seems to be a “normal” number (which means it behaves almost like if it was random), but there seems to be no proof of it yet.

You can try finding your name in pi. Big names are hard to find, though.

EDIT:

Sorry, but you guys are not quite right. If the sequence of digits is truthfully random, yes, but pi is generated by calculations.

For instance, this number, as simple as it seems, is irrational:

0.101001000100001000001…

You won’t find any 2’s, 3’s or 9’s in it, nor a sequence of 1’s longer than one digit. But it is also not a division of two integers, it goes on forever without repeating any sequence.

EDIT2:

That has absolutely nothing to do with numbers. And they have much less to do with the universe. By infinite numbers (in this thread) we don’t mean “one infinite number” but “infinitely many numbers”. Infinities are not considered to be numbers in math, because addition and multiplication are different than with numbers, while subtraction or division are not well defined. They are named cardinal… er… numbers, but that is just a name.

#208

Codgin, even if you ignore what everyone’s been repeating, what about +1?

#209

I’m not ignoring folk it’s just complicated and very hard to get your head around (Especially my own), it’s easy to say that numbers are infinite, that its perfectly innocent to say they are but the actual proof in the pudding is near impossible to provide and full of paradoxes. Such as for example the infinite universe. I wish I could explain or even understand it but I don’t lol. Even if you were to try and write an incredibly large number, eventually you’d have to stop and if someone carried it on, eventually somewere they will stop. And if one number is infinite like 1,2,3,4,5,6,7,8,9etc there could be another number that is bigger like 2,4,8etc that is infinite, so which is the true infinite? How can infinite be the biggest number when there is always a bigger infinite? Like if you have a hotel with an infinite number of rooms and you can’t get in one because they are all occupied, so you ask the owner to move everybody one room forward, infinty got bigger but how can infinty get bigger if its infinty? Saying the biggest number is infinity is easy but proveing it is a whole different ball game. So anyone care to explain how infinity is the biggest number and how that is even possible in a finite universe?

And before anyone trys to get smart and say 9 followed by an infinite number of 9s I’ll say this + 1. So my new infinite number is 10 followed by an infinte number of 0’s. How can infinty be the biggest number when you can just add one?

(Hopefully this will restore some credibilty for my arguement then my appalling logic previously lol)

#210

But what you’re saying has nothing to do with numbers not being infinite.

#211

I’m not saying numbers can’t be infinite I’m saying that infinite can’t be proved, and in relation to the “big” number infinty can not yet disprove there is an end number. No matter how big that number might be. Which is what this topic is about, to believe in infinity you would also have to accept that their may be an infinite universe and if we had an infinite universe, well shizzle gets messy

#212

I’ve just wasted an hour in my life to watch this stupid documentary and, what a surprise, it didn’t change my perception of reality. There was actually just one heretic (Doron Zeilberger) who claimed that there is The Biggest Number and when you add one to it you get zero. As it turns out he is a “worshiper” of something called Ultrafinitism - it has no logical nor mathematical basis whatsoever.

Oh, and one more thing - Codgin, no offense, but I think that you didn’t really understand all what they was talking about in this documentary. They didn’t say anything that infinity can exist in mathematics only if the Universe is infinite.

EDIT2: In this documentary they were saying something about comparing infinities - I’m not a mathematician, but for me doing such thing has as much sense as dividing by 0. There is no bigger or less infinities.

#213

#214

Damn it man you ninjad me :smiley:

#215

this thread could be interesting, it’s too bad you’re all talking about math

#216

Well, what you said makes sense if you think about numbers. There is, however, the problem with set cardinalities.

In mathematics, there is a standard and consistent way to compare two sets to see if one has more elements than another one. We can therefore associate the sets with objects which are called cardinalities.

But:

@Codgin: apparently you are getting the wrong idea here. You seem to be arguing that infinity can’t be considered as a number, which no one seems to be doubting here. The other issue, which others here are attacking, is whether there are only a finite amount of numbers. The two things are completely apart.

The former is just the definition of number, which is irrelevant, it is just the name you choose for your dog.

The latter comes to what you consider to exist. With ultra radicalism, you would say that a number can only exist if it can be physically represented with the limiter resources of our universe, that is called Ultrafinitism, a theory that fails when it comes to credibility, including to me.

The most accepted and coherent idea in mathematics is that infinite sets exist, and cardinalities is just the name you give to some particularly constructed sets that you choose to represent the amount of elements in a set, including finite sets. Sets of what, you ask? They are sets of… sets! These are also sets of sets. Just plain beauty! :wink:

Even numbers (with their standard operations) can be constructed from sets! We see no problem with that because the actual nature of numbers is mathematically irrelevant, what is important is the relations they have to each other. Set theory plays a beautiful role in this subject. We leave that other useless and objective-less discussion to philosophists :wink:

#217

Hmmm, so my intuition says that even if the cardinalities of two infinite sets are equal, it doesn’t mean that they have the same number of elements, because you cannot compare infinities. This may sound like rubbish, because the set cardinality is the number of elements of the set, but the problem is that the operators {=,<,>} are defined in a different way for cardinalities and for numbers. Does this make any sense?

#218

It does make sense, at least I could understand your point. Nevertheless, set cardinalities is consistent and well-accepted, it is just anti-intuitive, like zillions of things in math. For instance: the set of natural numbers have the same cardinality then the set of rational numbers, which means, in essence, that you can put all rationals in a line to get ice cream and count them all (this is how you do it). But the natural numbers are all rationals, and there are infinitely many more of these than just those! It goes against our reasoning, but it is consistent, that is what matters.

(BTW, there are very much crazier results than this one.)

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