How do you say $3\uparrow\uparrow\uparrow3$?

Question

How do you say $3\uparrow\uparrow\uparrow3$? English is my second language and I'm not sure how I should read it.

Answer 1

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

$$\underbrace{{\left(\underbrace{a^{a^{{\cdot}^{\cdot^{a^{}}}}}}_{\text{#} a\text{ times}}\right)^{{\left(\underbrace{a^{a^{{\cdot}^{\cdot^{a}}}}}_{\text{#} a\text{ times}}\right)}^{{\left(\underbrace{a^{a^{{\cdot}^{\cdot^{a^{}}}}}}_{\text{#} a\text{ times}}\right)}^{{\cdot}^{{\cdot}^{\cdot^{{\cdot}^{{\cdot}^{\left(\underbrace{a^{a^{{\cdot}^{\cdot^{a^{}}}}}}_{\text{#} a\text{ times}}\right)}}}}}}}}}}_{\text{#} a \text{ times}}$$

Answer 2

It should be read "3 three (or triple) arrow 3".

Reference at 2:35