Graham's number is so incredibly vast it defies conventional understanding, far exceeding the number of atoms in the observable universe, and can't be written out physically; it's defined through a recursive process using Knuth's up-arrow notation, building immense towers of exponents (3^3^3...) where the number of 3s in each subsequent tower is determined by the previous one, resulting in a number that's astronomically larger than even a googolplex.
The Magnitude and Representation of Graham's Number
That's roughly a number with 80 zeros. Graham's Number isn't just bigger; it's so vast that even writing all its digits would require more space than the universe itself.
In fact, not only is Graham's number so large that its digits can't be written out within the size of the universe, but neither can the number of those digits, and neither can the number of digits in that number, and so on all the way down, for more levels than the total number of Planck volumes in the observable ...
In other words, G is calculated in 64 steps: the first step is to calculate g 1 g_1 g1 with four up-arrows between 3s; the second step is to calculate g 2 g_2 g2 with g 3 g_3 g3 up-arrows between 3s; the third step is to calculate g 3 g_3 g3 with g 2 g_2 g2 up-arrows between 3s, and so on, until finally calculating G = ...
Using this algorithm with hand computations on paper, Lucas showed in 1876 that the 39-digit number (2127 – 1) equals 170,141,183,460,469,231,731,687,303,715,884,105,727, and that value is prime. Also known as M127, this number remains the largest prime verified by hand computations.
A vigintillion is a massive number, most commonly defined in the short scale as 1 followed by 63 zeros (106310 to the 63rd power1063), making it one thousand novemdecillion, though historically and in the long scale (used in some European countries), it could mean 1 followed by 120 zeros (1012010 to the 120th power10120). The modern standard in English-speaking countries uses the short scale, where a vigintillion is 1,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,0001 comma 000 comma 000 comma 000 comma 000 comma 000 comma 000 comma 000 comma 000 comma 000 comma 000 comma 000 comma 000 comma 000 comma 000 comma 000 comma 000 comma 000 comma 000 comma 000 comma 000 comma 0001,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000.
Infinity plus one is still infinity. This is precisely the same principle as in Hilbert's Hotel above, where we paired up the infinitely many room numbers with the infinitely many guests. = {…,–3 ,–2, –1, 0, 1, 2, 3, …}).
This sequence does not extend above 52 because it is, an untouchable number, since it is never the sum of proper divisors of any number. It is the first untouchable number larger than 2 and 5.
TREE(3) is a colossus, a number so large that it dwarfs some of its gargantuan cousins like a googol (ten to the one hundred), or a googolplex (ten to the googol), or even the dreaded Graham's number (too big to write).
Yes, Google is a misspelling of "googol," a mathematical term for the number 1 followed by 100 zeros, which founders Larry Page and Sergey Brin chose to represent the vast amount of information they aimed to organize. The name stuck after a friend, Sean Anderson, accidentally typed "google.com" instead of "googol.com" while checking domain availability, and Page liked the sound of the misspelled word.
Yes, an octillion is a very large number, representing 1 followed by 27 zeros (102710 to the 27th power1027) in the short scale (used in the U.S., Canada, and France) or 1 followed by 48 zeros (104810 to the 48th power1048) in the long scale (used in Britain and Germany). It's part of the naming system for large numbers that continues from million, billion, trillion, and so on, used in science and finance, although powers of ten are more common in science.
The cardinal number of one quintillion is 1,000,000,000,000,000,000. We can say that a quintillion is a million million millions or a billion billions or a million trillions or a thousand quadrillions.
As much as we would like to have an answer for "what's 1 divided by 0?" it's sadly impossible to have an answer. The reason, in short, is that whatever we may answer, we will then have to agree that that answer times 0 equals to 1, and that cannot be true, because anything times 0 is 0.
Googol is 10 to the 100th power, which is 10,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000, 000,000,000,000,000,000,000,000,000. Googolplex isn't just that number but has that many zeros in it. It simply has no other nameable name.
According to global superstitions, the unluckiest numbers are 12, 17, 13 and 666. The Japanese culture also believes some ages to be unlucky including 25, 42 and 60.
70 is the smallest weird number, which is a natural number that is abundant but not semiperfect. 70 is also part of the only nontrivial solution pair to the cannonball problem, along with 24.
Despite common misconceptions, 0.999... is not "almost exactly 1" or "very, very nearly but not quite 1"; rather, "0.999..." and "1" represent exactly the same number. There are many ways of showing this equality, from intuitive arguments to mathematically rigorous proofs.
Is Omega bigger than infinity? There is no correlation between omega and infinity since there is no last number in the infinite set.
I was watching Numberphile's video on how TREE numbers work and in the video they said TREE(3) is much more massive than Graham's number (effectively Graham's number would be 0 compared to TREE(3)). They said that it is known that TREE(3) is not infinite but there is currently no known upper-bound.
None of the words jillion, zillion, squillion, gazillion, kazillion, bajillion, or bazillion (or Brazilian) are real numbers. In the last two cases above, you'll notice that instead of an equals symbol we've used a squiggly equals symbol.
Quattuorvigintillion. A unit of quantity equal to 1075 (1 followed by 75 zeros).
A unit of quantity equal to 10183 (1 followed by 183 zeros).