Really Big Numbers
 

Today I wrote out every digit of 1000! However, the correct term for the result is four bagillion.

Does any else have any really big numbers they would like to share?

A googleplex - one with (one with a million zeros) zeros.

42

what else?

7

Play Marathon, you might notice it.

# 10 characters

Attachment 272 + 1

:whistling:

I raise you with http://img380.imageshack.us/img380/5144/infinityco8.jpg + http://img380.imageshack.us/img380/5144/infinityco8.jpg

http://img380.imageshack.us/img380/5144/infinityco8.jpg multiplied by http://img380.imageshack.us/img380/5144/infinityco8.jpg

according to mathematics, the only person who was correct about the unlimited was tomekk
unlimited+1=still unlimited
unlimited+unlimited=still unlimited
unlimited*unlimited= unlimited of higher range

OK.. OK.. http://img380.imageshack.us/img380/5144/infinityco8.jpg ^ (to the power) http://img380.imageshack.us/img380/5144/infinityco8.jpg ==> http://img410.imageshack.us/img410/2...finity2on7.png

Let us try another way.

The conclusion is that the biggest number is 1

I'm going to go with pi.

3.14159 ad infinitum

I remember watching some show years ago that tried to explain that mathematically speaking, a traveling object could never reach its destination, but could come infinitely close. The equation you're using is basically the outcome. Totally illogical to me, but maybe you're right in that sense, and 1 really is the biggest number.

huh? the conclusion is that the biggest number is 3

3
:P

That's not really the way it works, infinity is neither a real nor a definite number.

By the way the total numbers of atoms in the whole universe has been estimated at around 1e80, so chances are that you won't need one bigger. :P

Not true, that paradox was solved centuries ago. That you divide a process in infinite steps does not imply that it will take an infinite amount of time, since an infinite number of amounts can add a finite amount:

http://en.wikipedia.org/wiki/Convergent_series

:omg: Japo, Why are you tossing that stuff onto me? I can't read that gibberish! :)

I was a kid back then, so can't remember details. I just remember that they tried to explain mathematically that a ball thrown from a pitcher would never actually reach the catcher, because for each instance of time, the ball would only travel half as far as the previous time. I don't know how that's logical, or what the heck it has to do with baseball. It's confounded me to this day. :embarassed:

These kind of paradoxes were formulated by charlatan Zeno on the Vth century BC. The one I heard first was "Achilles and the tortoise":

But if you calculate the sum of that infinite amount of ever shorter time spans, the total is finite. Just the same that

1/2 + 1/4 + 1/8 + 1/16 + ... = 1

Even though there are infinite addends, they add up a finite amount.

Today I put 10 000! into my calculator which broke it... However, 2000! worked fine:nuts:

That's only theoretical -> e.g. 1 is the sum to infinity of that sequence. In what could be called 'practical terms' e.g. no theoretical numbers such as infinity, Achilles will never pass the tortoise. Of course, taking exact points in time for a continuous scale doesn't have any bearing in real life, but from the standpoint of conventional maths, 1 is never reached.

well, it's a set, which has infinite ammount of numbers, so..

No, infinity isn't certainly a set, it's not the whole field of real numbers --and it's none of them either. Infinity could be thought of as a single number two numbers (plus and minus infinity, although with complex limits it's different), but it's actually a concept that appears only when talking about limits, so everybody misunderstands infinity as a mathematical concept or number.

But it was you (or Zeno) who broke up whatever into infinite parts for no good reason. Everything can be broken up into infinite parts. You can be thought of as made up of infinite hypothetical parts, then it must mean that you cannot exist or that you cannot be contained or something stupid.

You can calculate how and when Achilles will pass the tortoise without contemplating any infinite sequence, just in one step. The fact is however that if you insist on calculating the time for each of the infinite time spans and add them up, you get the same result. BTW that is what maths is about, you always get the same result, the true result, no matter how. Very unlike speculation, or so-called "philosophy".

Arguing philosophically against something proven by maths or experience is a sure way to embarrass oneself... And I will henceforth stay away from the philosophical side of this topic, since philosophy = pseudo-science. :amused:

phislosophical response
 

I think one is the biggest number. AS the wizard in the movie fable showed us all the power in the world is concentrated in the oneness aspect of oneself. That makes one a really big number if you measure the effect of one person on the course of society.

first of all, nobody said that infinity is a number (?). and then, infinity can be as well declared as a set with infinite amount of objects

Here, we will never have the chance to what the biggest number in the world is, cause it goes on forever....

You already said that but I'm afraid I don't follow...

Not the mathematical "infinity" usually represented by
http://img380.imageshack.us/img380/5144/infinityco8.jpg
As in, "Achilles must traverse an infinite number of points before catching up to the tortoise", or in, "when x tends to 0, 1/x² tends to infinity". I think that's what we were talking about.

Maybe to consult: http://en.wikipedia.org/wiki/Democritus

japorfan infinity is not only used or defined in function limits=S

When I was still maried, and came home drunk after a drinking party with friends.
Infinity:
My wife nagging, and nagging , and nagging, and nagging, and nagging , and nagging, and nagging, and nagging , and nagging, and nagging, and nagging , and nagging, and nagging....

Big fleas have little fleas upon their backs to bite them
Little fleas have smaller fleas and so on ad infinitum

I feel the need to present some sort of consensus. This is how it is done at my school (University of Toronto).

what you posted is already here in this thread :p

I accidentaly figured out two different sized infinities. There are an infinite number of prime numbers. There are also an infinite amount of numbers which are not prime. However, at any given point after 10, the number of prime numbers will be smaller than the number of not prime numbers. Hence, a smaller infinity. Trippy, huh?

nope, exactly the same range infinity

Yeah, you're right... both sets have a cardinality of aleph-null. It's just so weird though. At 10, there are 5 primes and 5 not primes. At 20 the ratio is 9:11. At 30, the ratio is 11:19. The prime numbers NEVER catch up! How can their infinities be the same size????

it's infinity it doesn't have "size" :D

From above...In the context of measuring sizes of sets,
in which "infinity" means a measurement of the size of an infinite set. In this context, such "infinity" concepts do exist but there are more than one of them, since not all infinite sets have the same size. So there does not exist any one single "infinity" concept; instead, there exists a whole collection of things called "infinite cardinal numbers".

The question is about the cardinality (aka size) of those two sets.

According to that, the size (cardinality) of the set of prime numbers would be the same that the set of non primes, and the same that the set of all natural numbers, etcetera:

This concept is different from the other, and pertains to set theory.

If you ask me, the biggest number is the Atlantic Ocean. It's kind of a 5.

yes that's what we were basically talking about

WTF? How can an infinite set be smaller than another infinite set? They're both infinite! They both have an infinite amount of numbers!

try imagining it on dimensions. 1d line, 2d whole plane and brand new dimension, 3d next noncollinear vector and you've got another dimension with volume

They're only concepts from set theory, which is based on certain axioms. Axioms are principles that can't be proven, but serve as foundation for the theory. So the theory holds true only after the axioms are accepted as true. And the theory's useful in the extent that those axioms can be applied to real concepts.

The point is, the cardinality of infinite sets is a completely different concept from the concepts of infinity we were discussing before. Let's not mix separate concepts.

we were talking about big numbers and then somebody mentioned infinity, we didn't have any rules about not discussing infinite sets=S

actually an infinite set is quite a biggie if you ask me

Yes yes I didn't call off topic, I'd be as guilty as anyone. :P But if we are discussing about all this at the same time we shouldn't confuse different concepts referred to with the same word.

BTW: http://en.wikipedia.org/wiki/Hilbert...he_Grand_Hotel

Another way to imagine the differences between infinities is on a number line. The set of real numbers is infinitely larger than the set of integers for instance.

This topic is filled with infinite LULZ.

The concept of infinite is a loop, if I could see in a infinite view (if there was nothing blocking my view) i would see the back of my head.

That is how infinite was explained to me....

Infinite is NaN in real world and only expressible on paper and theory?

Lots of simple meaningless threads are becoming intellectual discussions here.:omg:

I love this place lots of smart people.:cheesy:


Anyways 9 is the biggest number, where all other Numbers are based on. *walks away with a headache*

You wouldn't see the back of your head. To do that, your sight would not need to be infinite, but curved over the surface of the Earth. And the concept of infinity can not be proved or disproved in physical terms because the human mind has no capacity for comprehending an infinite distance or an infinite set of numbers or objects.

And yes, this place is overflowing with smart people. :thumbs:

Actually, there are as many integers as there are primes. They are both countable sets. Between any two integers, or any two primes, there are only a finite number of elements. A bigger infinity is the set of real numbers. Not only is there an infinite number of them, but there is an infinite nmber of distinct real numbers between any two elements.

The bit with Achilles and the tortoise is that while there are an infinite number of slices of time with Achilles not cathing up to the tortoise, the sum of the durations of that infinite number of instances is a finite number. If the tortoise has a 100 meter head start and scampers at the un-tortoiselike speed of one meter per second to Achilles leisurely (for Achilles) ten meters per second, the total duration of all those instants of time one hundred nineths of a second, for a total distance of one nineth of a kilometer

Is there a smiley dictatiing an exploding head? Oh, well, let's have a go ... :boom:!

Oh dear *goes crosseyed* ... I think I've just gone crosseyed... :wacko:

Infinity is not a number, it's a concept.

kugerfang how about you read the topic before posting and making yourself look funny

It really is a number, it is just a really big number. One of the early problems in quantum mechanics is that infinity kept showing up in the calculations, normally of the form infinity = infinity. As this did not allow for any meaningful analysis, they 'renormalised' the equations by dividing both sides by infinity. Since the infinity on each side of the equation was of the same order, this allowed for meaningful calculations with finite results-- that matched experimental observations. Quantum gravity had the problem (I took a course in elementary particle physics eighteen years ago [and discovered that the particles were elementary, not the physics], and they may have solved it by now) that dividing both sides by infinity still had infinities on both sides.

It should be mentioned that dividing by infinity was not the straightforward task like dividing a number by two, but first coming up with a creative method of composing an expression that equals infinity and dividing by that (similar to constructing innovative ways of multiplying by one, or adding zero, in Algebra)

Never let anyone tell you that a degree in mathematics is entirely useless!

Oh yeah, indeed, and the lulz is really neverending.
:nuts:

tssssss ...
:BOOM:!

Here is a neat site on the set of prime numbers.
infinity
I found it by exploring this incredible site