Equality of sets

[Xiaoquan Li]

In ploycomu-tutorial-v0.02.pdf, page 48

Example 3.29

{a[n,i] : 0 ≤ i < n} 

{a[m,i] : 0 ≤ i < m}

Why they are equal? If m has different value with n, it seems they contains different pairs

 Thanks

[Sven Verdoolaege]

On Tue, Dec 06, 2022 at 06:20:10PM -0800, Xiaoquan Li wrote:
> In ploycomu-tutorial-v0.02.pdf, page 48
>
> Example 3.29
>
> {a[n,i] : 0 ≤ i < n}
> {a[m,i] : 0 ≤ i < m}
>
> Why they are equal?

As mentioned in that example, these two sets contain the same pairs
of integers.

> If m has different value with n, it seems they contains
> different pairs

Both m and n can have an infinite number of values,
but the sets of values (paired off with the corresponding
values of i) are the same.

Note that m and n are not (symbolic) constants here.
They are variables, just like i.

Admittedly, the difference is a bit subtle in the mathematical
notation, with roman font for constants and italics for variables,
but in the textual isl notation, the parameters are listed explicitly,
so it should be clear that m and n are not constants in 3.29.

skimo