The googolgoogoltriplex or googolstackstackstack[1] is equal to \(10 \uparrow\uparrow 10 \uparrow\uparrow 10 \uparrow\uparrow (10^{100})\). or \(10 \uparrow\uparrow \text{googolduduex}\)[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 | \(\textrm{E}100\#1\#4\) |
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.
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