Try to explain the 'worlds largest number(s)' in a way that everyone can understand?

Question

By worlds largest number(s), I mean the largest number(s) that have ever been used in mathematical proofs (which is the accepted definition). Try to make these generally unfathomable numbers understandable.

10 points for best description (using infinity is not allowed).

By 'used in a proof', I mean the numbers that are often used as upper limits or lower limits when the number range involves phenomenally large numbers. That is the way mathemeticians define "worlds largest number" - it is the biggest number that can be shown to be a limit in a math proof.

For example, Skewes number is 10^10^10^32 power. Its no where near the largest, but it is so large that if you filled the entire universe with hydrogen sized zeros every second of time from dawn of time until now, and put a 1 in front, you would not even be close. Think BIG!

Answer 1

The title of "world's largest number" is generally given to Graham's number, named after Ron Grahom. It's enormous. It arises as an upper bound in a problem from Ramsey theoretic graph theory, like a lot of very large numbers. These numbers sometimes arise when someone is trying to prove that something exists and they try doing so using probability.

Here's a heuristic:

If you are looking in a box full of balls and want to pick out a handful of them such that when they are all put together they have some desirable quality, the easiest way to make sure that you can find such a handful is to put a lot of balls in the box. The more balls that are in the box, the more handfuls there are to choose from and the more likely it'll be that you find a handful you like. Now imagine that you can only be certain that you like the balls if none of them had touched each other in the box before you picked them. You may pick up a handful that you would have liked but if they had touched then you wouldn't be able to tell so you would have to keep looking. Now, the easiest way to make sure you can find a handful you know you like is to put so many balls in the box that there are tons of good handfuls. If you are very picky and very indecisive about which balls you like then you'll need a very large number of balls.

I'm not certain that Graham's number arose in this way but it's likely. If you want to read up on it try http://mathworld.wolfram.com/GrahamsNumber.html or http://en.wikipedia.org/wiki/Graham%27s_number
and while you're at it, read Ron Graham's bio on Wikipedia. He's an interesting fellow.

Answer 2

You can get as far away from zero as you want, but you'll never even get near infinity. You cannot put infinity and zero on the same line because, by mathematical nature, they are both the same number!
Zero has a negative infinity and infinity, of couse is positive by nature.
For the purpose of understaning, there is no "world's largest number" if you did happen to find such a thing, you could always add another digit...always. There is no number that cannot be made larger than it already is and that- is the final answer

Answer 3

Claiming that a god is an exception and does not need to have been created because said god is all powerful is fallacious because it is entirely dependent on the circular reasoning to believe in a god. Speaking of which, if somehow you convince us that the world was created by a higher being, how do you prove it was the christian god? Other religions tell their own stories and yet you claim them false. How do you prove one creation story over another? The bible says the christian god is eternal, i will accept that premise. But how do you know you can trust the bible? If your answer is anything along the lines of "it is God's book" (even if it takes a few steps to reach it) then you are guilty of circular reasoning. The bible cannot simultaneously be a premise and a conclusion. The fact a pastor prayed for you and then you got better is entirely post hoc ergo propter hoc. Further, why is it that other families just as Christian as yours pray for their children to survive a condition but the child does not? If it is God's plan to kill or if he works in mysterious ways when something bad happens but he is so great when something good happens, then you are guilty of selective attention. You say you had plenty of evidence. What evidence? Just feeling/knowing it, having experienced the holy spirit for yourself is not evidence because it is not something that can be identically recreated in a controlled environment. The fact you quit drugs and alcohol is great but you decided by yourself. It was all you. Religion may have helped but it certainly cannot be directly credited as the sole cause. Want to make God happy? Well you cannot just choose the nice parts of the Bible. Oh and you cannot ignore the old testament because as you know, Matthew 5:17 says "Think not that I am come to destroy the law, or the prophets: I am not come to destroy, but to fulfil." So then all of the Leviticus business about things being prohibited apply to you. And why not listen to Acts 3:23? It says "And it shall come to pass, that every soul, which will not hear that prophet, shall be destroyed from among the people." What about Romans 5:12? It says "Wherefore, as by one man sin entered into the world, and death by sin; and so death passed upon all men, for that all have sinned: And read 2 Thessalonians 1:8. "In flaming fire taking vengeance on them that know not God, and that obey not the gospel of our Lord Jesus Christ:" I could go on with some passages but the point I made is clear: there are many negative things in the bible that you fail to address. Why do you ignore them? Why are those things necessarily metaphorical while the good things are necessarily to be taken relatively literally? You being happy may be a result of having found religion but it is not evidence of it. Statistically speaking the happiest nations tend to be more Atheistic (among them are Norway, Sweden, Australia, and Canada). Now these statistics don't prove that a god does not exist nor does it prove a more atheistic nation is necessarily happier or better off. It does, however show a correlation. Regardless of this, NOTHING you said proves any god exists. Let me bring you this hypothetical scenario: if I were wounded and decided to ask Apollo, the ancient Greek god who in addition to being a sun god was also known as a healer, to help me. And then I am cured. Does that prove that Apollo and the other greek gods exist? Of course not. The reason is not because it is thanking a god different than your own but because you would want proof. Much like that, nonbelievers ask for proof. Your claims are just claims. These claims cannot be recreated. Science does not truly know how life began and it might never know. However the fact science is willing to admit ignorance shows that it accepts it does not know everything and that it is willing to change. Every scientific discovery is fair game for debunking. If it can be conclusively and scientifically proven a god exists and created everything we know then the scientific community will accept it.

Answer 4

The best interpretations of large numbers came from Carl Sagan and a video I saw at a science convention.

You may have seen the video... it shows distances starting at a meter using exponential growth and decay... it amazed me how tiny things are in atoms yet spread out, and how far away things are in space.

Carl famously pointed out that there are more stars in the Universe than there are grains of sand on all the beaches of the world... just think of how many grains are in a handful... on one beach!

The movie Mindwalk does a good job of explaining things similarly to how the video does... as well as how things interact with one another.

In my explanations I tend to try to connect the numbers to things people are more familar with. For instance we all know to give astronomical distances in light years rather than kilometers or parsecs because people then think... if I could go at the speed of light, which I can't... I wouldn't even get to that star for another 10 years (or whatever).

When I told people how large the smallest brown dwarf stars are I didn't just say "1.9*1028 kilograms" that is about 10 times the mass of Jupiter, which, since people somewhat understand the greatness of Jupiter through other scales (like to Earth) is much easier to comprehend.

Besides when you say things like how a planet would float in a bathtub big enough, it helps people realize just how phenomenal our universe is.

Answer 5

The largest number I can think of is googol-plex, which is one followed by a googol number of zeros (one googol is one followed by one hundred zeros). These numbers count as numbers that are so large that they are "beyond the lifetime of a universe". Indeed, there aren't even a googol number of atoms in the Universe (there are about 7 * 10^78 by some estimates). So therefore if you took all the zeros in a googol-plex, there wouldn't even be enough subatomical particles in the universe for each zero.

Answer 6

Each number keeps adding on. Like a timer that may be counting up, numbers continue to rise and add on to the end as well. Also includes a decimal point which makes the numbers to the right increase as well. That's the best I got. haha

Answer 7

The world's largest number can be described by or referred to as the number of grains of sand that there is in the world or the number of stars in the sky.

Answer 8

Sorry to burst your bubble... but no 'numbers' are used in proofs.

Proofs involve general situations. If i were talking about an arbitrarily large integer i would call it N.

So i guess by that token, any arbitrarily large enough arbitrary number 'N' is the largest :P

Answer 9

The equation for a fractal is; X^2 + y. Fractals are never ending self similar forms. " any subsystem of a fractal system is equivalent to the whole system. " A Mathematician named Benoit Mendelbrot discovered this. He describes fractals as a way of seeing Infinity.

Answer 10

Avogadro's number is a pretty large one. It's 6.02x10^23 and its the number of atoms, molecules, or anything really in a mole.