The googolgoogoltriplex or googolstackstackstack[1] is equal to \(10 \uparrow\uparrow 10 \uparrow\uparrow 10 \uparrow\uparrow (10^{100})\).[2]
Aarex Tiaokhiao calls this number googoltreduex.[3]
Username5243 calls this number googoltriduex, and it's equal to 10[2]googolduduex in Username5243's Array Notation.[4]
Etymology
The name "googolstackstackstack" can be separated into 4 parts, "googol" and 3 "-stack"s, where "n-stack" means \(10\uparrow\uparrow n\), so 3 "-stack"s means the operation applying 3 times.
Approximations in other notations
| Notation | Approximation |
|---|---|
| Up-arrow notation | \(10 \uparrow\uparrow 10 \uparrow\uparrow 10 \uparrow\uparrow 10 \uparrow 100\) (exact) |
| Chained arrow notation | \(10 \rightarrow (10 \rightarrow (10 \rightarrow 10^{100} \rightarrow 2) \rightarrow 2) \rightarrow 2\) (exact) |
| BEAF | \(\{10,\{10,\{10,\{10,100\},2\},2\},2\}\) (exact) |
| Hyper-E notation | \(E100\#1\#4\) |
| Hyperfactorial array notation | \((((70!)!1)!1)!1\) |
| Fast-growing hierarchy | \(f_3(f_3(f_3(f_2(324))))\) |
| Hardy hierarchy | \(H_{\omega^33+\omega^2}(324)\) |
| Slow-growing hierarchy | \(g_{\varepsilon_{\varepsilon_{\varepsilon_{\omega^\omega}}}}(100)\) |
Sources
- ↑ Cantor's attic
- ↑ bigΨ section 1.5.2. Googol world
- ↑ Part 1 (LAN) - Aarex Googology
- ↑ Username5243. Part 1 - My Large Numbers. Retrieved 2017-01-15.
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.
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