9

Properties

• 9 is also equal to !4 using subfactorial.
• Its prime factorization is 9 = 3².
• 9 is one of two known odd unitary superperfect numbers. The other one is 165.
• A 9 sided polygon is called an enneagon or a nonagon.

In googology

• Some googologisms based on 9 are googolnoniplex and superenn.
• 9 can be named "garthree" with the gar- prefix.
• In Greek-based number naming systems, 9 is associated with prefix ennea-, and with prefix nona- or novem- in Latin systems
• Username5243 coined the name Ternary-Goodol for this number, and it's equal to 3[1]2 in Username5243's Array Notation.^[1]

Googological functions returning 9

• Gijswijt's sequence: \(c(3)=9\)
• Laver table: \(q(4)=9\)
• Mixed factorial: \(3^*=9\)
• Expostfacto function: \(\mathrm{expostfacto}(3)=9\)
• Exponential factorial: \(3!1=9\)

Sources

1. ↑ Part 1 - My Large Numbers