- "Googolduduex" redirects here. It is not to be confused with googoldudex.
Googolstackstack is equal to \(10\uparrow\uparrow \text{googolstack}\) or \(10 \uparrow\uparrow 10 \uparrow\uparrow (10^{100})\).[1] It is also called a googolgoogolduplex.[2] It is equal to a power tower of googol-stack tens.
Aarex Tiaokhiao and Username5243 call this number googolduduex.[3][4]
Etymology
The name "googolstackstack" can be separated into 3 parts, "googol" and 2 "-stack"s, where "n-stack" means \(10\uparrow\uparrow n\), so 2 "-stack"s means the operation applying 2 times.
Approximations in other notations
| Notation | Approximation |
|---|---|
| Up-arrow notation | \(10 \uparrow\uparrow 10 \uparrow\uparrow 10 \uparrow 100\) (exact) |
| Chained arrow notation | \(10 \rightarrow (10 \rightarrow 10^{100} \rightarrow 2) \rightarrow 2\) (exact) |
| BEAF | \(\{10,\{10,\{10,100\},2\},2\}\) (exact) |
| Hyper-E notation | \(E100\#1\#3\) |
| Hyperfactorial array notation | \(((70!)!1)!1\) |
| Fast-growing hierarchy | \(f_3(f_3(f_2(324)))\) |
| Hardy hierarchy | \(H_{\omega^32+\omega^2}(324)\) |
| Slow-growing hierarchy | \(g_{\varepsilon_{\varepsilon_{\omega^\omega}}}(100)\) |
Sources
- ↑ Cantor's Attic
- ↑ bigΨ section 1.5.2. Googol world
- ↑ Part 1 (LAN) - Aarex Googology
- ↑ Username5243. Part 1 - My Large Numbers. Retrieved 2017-02-25.
See also
0-stack series: googol · googolplex · googolbang · googolplexplex · googolplexbang · googolbangplex · googolbangbang · googolplexplexplex · googolplexplexbang · googolplexbangplex · googolplexbangbang · googolbangplexplex · googolbangplexbang · googolbangbangplex · googolbangbangbang
1-stack series: googolstack · googolstackplex · googolstackbang · googolstackplexplex · googolstackplexbang · googolstackbangplex · googolstackbangbang · googolplexstack · googolplexstackplex · googolplexstackbang · googolbangstack · googolbangstackplex · googolbangstackbang · googolplexplexstack · googolplexbangstack · googolbangplexstack · googolbangbangstack
2-stack series: googolstackstack · googolstackstackplex · googolstackstackbang · googolstackplexstack · googolstackbangstack · googolplexstackstack · googolbangstackstack
3-stack series: googolstackstackstack
Megoogol · Meg-Googol · Meg-Doogol · Meg-Kiloogol · Meg-Kil-Googol · Meg-Dukiloogol · Meg-Trukiloogol · Dumegoogol · Dumeg-Googol · Dumeg-Kiloogol · Dumeg-Dukiloogol · Trumegoogol · Trumeg-Kiloogol · Tetrumegoogol · Pentumegoogol · Gigoogol · Gig-Googol · Gig-Kiloogol · Gig-Megoogol · Dugigoogol · Trugigoogol · Teroogol · Duteroogol · Truteroogol · Petoogol · Ectoogol · Zettoogol · Yottoogol · Xennoogol · Wekoogol
Note: The readers should be careful that numbers defined by Username5243's Array Notation are ill-defined as explained in Username5243's Array Notation#Issues. So, when an article refers to a number defined by the notation, it actually refers to an intended value, not an actual value itself (for example, a[c]b = \(a \uparrow^c b\) in arrow notation). In addition, even if the notation is ill-defined, a class category should be based on an intended value when listed, not an actual value itself, as it is not hard to fix all the issues from the original definition, hence it should not be removed.