How do you say $3\uparrow\uparrow\uparrow3$? English is my second language and I'm not sure how I should read it.
Asked
Active
Viewed 279 times
7
-
1What does it mean? Where did you find it? – gen-ℤ ready to perish Aug 03 '19 at 16:53
-
1Maybe you mean $3^{3^{3^3}}$ If so you could use the term "to the power" or "exponent" – NoChance Aug 03 '19 at 16:55
-
1Also related is this:https://en.wikipedia.org/wiki/Knuth%27s_up-arrow_notation – NoChance Aug 03 '19 at 17:10
-
Three pentated with itself. – Lucian Aug 04 '19 at 01:00
2 Answers
3
The phrase literally means "$a$ triple uparrow $a$".
Mathematically this is Knuths up-arrow notation. In a simpler case, $a \uparrow \uparrow a$ means $a$ exponentiated $a$ times. $$\underbrace{a^{{a}^{{a}^{{\cdot}^{{\cdot}^{{\cdot}^{a}}}}}}}_{\text{#} a \text{ times}}$$
This is also called teration.
In your case, $a \uparrow \uparrow \uparrow a$ is the iteration of tetration, which is $a \uparrow \uparrow(a \uparrow \uparrow a)$ or
$$\underbrace{{\left(\underbrace{a^{a^{{\cdot}^{\cdot^{a^{}}}}}}_{\text{#} a\text{ times}}\right)^{{\left(\underbrace{a^{a^{{\cdot}^{\cdot^{a}}}}}_{\text{#} a\text{ times}}\right)}^{{\left(\underbrace{a^{a^{{\cdot}^{\cdot^{a^{}}}}}}_{\text{#} a\text{ times}}\right)}^{{\cdot}^{{\cdot}^{\cdot^{{\cdot}^{{\cdot}^{\left(\underbrace{a^{a^{{\cdot}^{\cdot^{a^{}}}}}}_{\text{#} a\text{ times}}\right)}}}}}}}}}}_{\text{#} a \text{ times}}$$
Arbuja
- 1
2
It should be read "3 three (or triple) arrow 3".
Reference at 2:35
gen-ℤ ready to perish
- 6,610
Cornman
- 11,065
- 4
- 30
- 57