What Does The Notation of Union Over K represent? I am currently studying about polynomial time in Comp Theory. The definition for polynomial time given in my textbook as follows:
$$P= \bigcup_{k}TIME(n^k)$$
I have not seen the Union over k notation before. K is a constant. A quick introduction to the meaning of this notation would be enormously helpful.

Thank you
Authors often leave out the domain of the union if it is clear within the context. Here, $k$ is a natural number, i.e. $P = \bigcup\limits_{k \in \mathbb{N}} TIME(n^k) $. This is what it means for a complexity function to be bounded by a polynomial: there is a constant $k$ such that the function is in $\mathcal{O}(n^k)$.