I was reading some papers and they had the following notation:
$$ \big\{k\big\}_{k=0}^n $$
I assume this implies that
$$ \big\{k\big\}_{k=0}^n = \{k \in \mathbb{WHAT} : 0 \leq k \leq n\} $$
What is $k$ an element of? I assume integers, but it might as well be real or complex. I propose a better, less ambiguous notation:
$$ \big\{k \in \mathbb{SOMETHING}\big\}_{k=0}^n $$
Would this work better or does this mean something completely different?
The notation $\{f(k)\}_{k=0}^n$ in the context given means either the sequence or set $$f(0),f(1),f(2),\dots,f(n) $$
in analogy to sum or product notation, where $$ \sum_{k=0}^nf(k)=f(0)+f(1)+\dots+f(n)$$
and $$\prod_{k=0}^nf(k)=f(0)\times f(1)\times\cdots\times f(n) $$
Your notation $\{k\}_{k=0}^n$ would mean $\{0,1,\dots, n\}$, but I think the paper is actually using examples like $\{\mathbf{c}_j^{(t)}\}_{j=1}^k=\{\mathbf{c}_1^{(t)},\mathbf{c}_2^{(t)},\dots,\mathbf{c}_k^{(t)}\}$.
Context should indicate whether order is important, if distinguishing between sequences and sets is key.
Instead of your notation, what you might see instead is $\{f(k)\}_{k\in S}$ for some set $S$, again in analogy to sum or product notation.
