What does $\mathbb{Z}[[t]]$ mean? Why are there double square brackets?
I can't search through Google, because I can't search Latex.
What does $\mathbb{Z}[[t]]$ mean? Why are there double square brackets?
I can't search through Google, because I can't search Latex.
That is the ring of formal power series in $t$ with integer coefficients, i.e., of $\sum_{n=0}^\infty a_nt^n,$ with $a_n\in\Bbb Z$, componentwise addition, and multiplication appropriately defined.
The double brackets distinguish it from $\Bbb Z[t]$, which is the ring of polynomials in $t$ with integer coefficients. We can always evaluate the members of $\Bbb Z[t]$ for any complex value of $t$, but we generally can't evaluate members of $\Bbb Z[[t]]$ for $t\neq 0$. To my mind, the double bracket is a reminder that we need to leave the $t$ alone, and not worry about evaluation.
If $A$ is any ring, the notation $A[[T]]$ stands for the ring of formal power series with coefficients in $A$, i.e. the ring whose elements are the expressions $ a_0+a_1T+a_2T^2+a_3T^3+\cdots $ with the obvious sum and product.