what is the largest number in the world?

Answer 1

It is not "infinity", because infinity is not a number. If we need a real number, then the largest is the "transfinite number". It is a number.

Try reading an article about it in Wikipedia.

^_^

Answer 2

Despite popular usage Infinity isn't a number - so that isn't the answer (and you might also object that its not in the world in the sense it could not be written down on any world no matter how large it is).

Similarly 1/0 isn't a number. (And clearly infinity/0 isn't a number on two grounds).

With all due respect to the person who suggested that transfinite numbers are numbers, the various species of Aleph (http://en.wikipedia.org/wiki/Transfinite_number) are infinite and don't behave as numbers.

To take your question literally, the largest number 'in the world' would have to be the largest number that can be represented on Earth, despite it always being possible to simply add one to any largest number.

Suppose you could put every atom on the planet into one of two energy states, then you would be able to use the whole planet as a vast binary number (small problem - how could you read such a number, but I'll ignore that).

The mass of the earth is approximately 6x10^24 kilos.
Although it is just a rough approximation, let's say that the average atomic mass of the atoms composing the earth can be represented by Iron.
A mole of iron has a mass of 55.845 grams and contains approximately 6 x 10^23 atoms.
So in round figures the earth contains (6* 10^27) x (6 x 10^23)/56 atoms = 0.64 * 10^50 atoms.

So this would the LENGTH of the largest number you could represent using every atom as binary digit.

So the biggest number you could represent using the whole world as a counter in this way would be
10 to the power (1.8 x 10^50).

According to Wikipedia the largest natural number that mathematicians have a use for is 'Graham's Number' -
see http://en.wikipedia.org/wiki/Graham%27s_number#Definition_of_Graham.27s_number
for an explanation, but you will probably need a lot of paper, several pencils and an adequate supply of patience to even write down what the formula is for this number.

Answer 3

Whilst infinity is the largest theoretical number in the world, the largest number that could be written down would be only 10^10^87 since there are only 10^87 elementary particles in the whole universe. To write that number down would require every atom in the universe to represent a zero and to lay them all out in a row. Since a googolplex is 10^10^100, this number could never be written out in its entirety.

However, some people have said that a googolplex is the largest known number, but this isn't true since larger numbers are possible using only 6 digits instead of the 7 required to write a googolplex: like 9^9^9^9^9^9 which is much larger indeed.

And by the way: 9^9^9 is not as large as 9^99 for the three digit largest number as demonstrated badly above

Answer 4

1

Answer 5

n+1

Answer 6

There is no "largest number" (a real number) in the world (and I take it you aren't talking about complex numbers, because given two complex numbers z and w, you can't make sense of z>=w). For suppose that there was a "world's largest number", and let it be denoted by k.

Then, consider k+1. Then, as we are assuming that k is the world's largest number, we have k+1
Therefore, our original assumption (that there was some "largest number") must be false. Hence, there can be no "largest number in the world". This was an example of a "proof by contradiction", where you assume a result (such as the existence of the largest number in the world), and demonstrate that it leads to a contradiction, and is, therefore false.

I hope this is helpful!

Answer 7

googolplexian is the largest number in the world

Answer 8

Not many people know this, and it sounds paradoxical, but there are different sizes of infinity. They are expressed by the transfinite numbers aleph-0 (spoken as either aleph-null or aleph-nought) and aleph-1, developed as part of his writings on set theory by the German mathematician Georg Ferdinand Ludwig Philipp Cantor (March 3, 1845, St. Petersburg, Russia – January 6, 1918, Halle, Germany), who explored this mind-boggling territory for the first time.

Cantor's 1874 paper, "On a Characteristic Property of All Real Algebraic Numbers", marks the birth of set theory. Previously, all infinite collections had been (silently) assumed to be of "the same size"; Cantor was the first to show that there was more than one kind of infinity.

Cantor established the importance of one-to-one correspondence between sets, defined infinite and well-ordered sets, and proved that the real numbers are "more numerous" than the natural numbers.

He first showed that given any set A, the set of all possible subsets of A, called the power set of A, exists. He then proved that the power set of an infinite set A has a size greater than the size of A (this fact is now known as Cantor's theorem). Thus there is an infinite hierarchy of sizes of infinite sets, from which springs the transfinite cardinal and ordinal numbers, and their peculiar arithmetic.

ALEPH NUMBERS

Aleph-nought is by definition the cardinality of the set of all natural numbers, and is the smallest of all infinite cardinalities. A set has cardinality Aleph-nought if and only if it is countably infinite, which is the case if and only if it can be put into a direct "one-to-one correspondence", with the natural numbers. Such sets include the set of all prime numbers and the set of all rational numbers.

But there are more irrational numbers between 0 and 1 than Aleph-0 and Cantor defined that as Aleph-1.

So my point is: plainly the statement "the biggest number there is is infinity" is is need of revision, and more precision.

I am not suggesting this is an easy subject (far from it), but if people are here to learn something new then I hope I have opened their eyes, a bit!

Answer 9

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Answer 10

There is no largest number in the world. For any number, you can add one to it to get an even bigger number. So you can get numbers as large as you want.