1. ## Correctness

Say That In A Symbolic Definition Of A Set Powered To $n$, What Definition Is More Correct?

$S_n=\left\{\left(a_1,a_2\ldots,a_n\right)\mid\fora ll i\leq n,a_i\in S\right\}$

Or The More Extreme One:

$S_n=\left\{\left(a_1,a_2\ldots,a_n\right)\mid\fora ll i\in\mathbb{N},i\leq n\Rightarrow a_i\in S\right\}$

Personally I Think That The Usage Of $\Rightarrow$ Is A Bit Confusing Here?

2. Originally Posted by olekaiwalker
Say That In A Symbolic Definition Of A Set Powered To $n$, What Definition Is More Correct?

$S_n=\left\{\left(a_1,a_2\ldots,a_n\right)\mid\fora ll i\leq n,a_i\in S\right\}$

Or The More Extreme One:

$S_n=\left\{\left(a_1,a_2\ldots,a_n\right)\mid\fora ll i\in\mathbb{N},i\leq n\Rightarrow a_i\in S\right\}$

Personally I Think That The Usage Of $\Rightarrow$ Is A Bit Confusing Here?
Just writing $S_n=\left\{\left(a_1,a_2\ldots,a_n\right)\mid a_i\in S\right\}$ would suffice - there is no ambiguity as to what the $a_i$ could be.

Also, I believe it is considered bad practice to put implies arrows and the like in the right hand side. I may be wrong though.

3. By Imply Arrows And The Like Do You Mean Quantifiers Also?

BecauseI Find Them Useful Sometimes.