- Thread starter
- #1
- Mar 22, 2013
- 573
How can numbers be large enough? Well, that is easy enough to answer. Take the $\zeta$-function and note that it has a pole at $1$. Oh, no, wrong kind of answer - take the successor function from Peano axiom and note that any bijection $f$ from $\mathbb{Z}$ to $\{0, 1, \cdots, n\}$ must satisfy $f(n + 1) = f(k)$ for some $k \in \{0, 1, \cdots, n\}$, thus violating surjection and contradicting bijection property.
Nevertheless, not every large number is interesting. For example, "quattuordecillion" or $10^{45}$ is not listed in Collin's English dictionary (11th ed.), Cambridge online dictionary or in Oxford English dictionary (2nd ed. and new ed.).
The purpose of this thread is to simply list the large numbers, which are interesting enough. Everyone can post, and the rules are
My favorites are :
Feel free to add more,
Balarka
.
Nevertheless, not every large number is interesting. For example, "quattuordecillion" or $10^{45}$ is not listed in Collin's English dictionary (11th ed.), Cambridge online dictionary or in Oxford English dictionary (2nd ed. and new ed.).
The purpose of this thread is to simply list the large numbers, which are interesting enough. Everyone can post, and the rules are
- The number must be interesting enough.
- The number must be large enough (although "enough" can be ruled out if it is very interesting)
- The number should be computable.
- Existence of such numbers is not enough to be posted here, and ...
- The number should be explicitly written here, although abbreviations are accepted, i.e., $10^{100}$ (gogol).
- If possible, a short intro on the number mentioned would be nice.
My favorites are :
- Gogolplex, $10^{10^{100}}$. Larger than the number of Plank spaces that composes the observable universe.
- Monster number, the order of the Monster group : $808017424794512875886459904961710757005754368000000000$
- Skewes' number $e^{e^{e^{79}}}$, introduced by Skewes as an upper bound to the smallest occurring of $\pi(x) > \text{li}(x)$
- Not-so-large Johnston number $14228$. In Nathaniel's opinion, this is the first uninteresting number since this is the smallest with the property that no OEIS entry contains this.
Feel free to add more,
Balarka
.