# Correctness

• Sep 27th 2009, 07:46 AM
olekaiwalker
Correctness
Say That In A Symbolic Definition Of A Set Powered To $\displaystyle n$, What Definition Is More Correct?

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

Or The More Extreme One:

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

Personally I Think That The Usage Of $\displaystyle \Rightarrow$ Is A Bit Confusing Here?
• Sep 27th 2009, 08:23 AM
Swlabr
Quote:

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

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

Or The More Extreme One:

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

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

Just writing $\displaystyle S_n=\left\{\left(a_1,a_2\ldots,a_n\right)\mid a_i\in S\right\}$ would suffice - there is no ambiguity as to what the $\displaystyle a_i$ 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.
• Sep 27th 2009, 09:15 AM
olekaiwalker
By Imply Arrows And The Like Do You Mean Quantifiers Also?

BecauseI Find Them Useful Sometimes.