Integers are a set of numbers with no upper or lower bound. There is no such thing as a first integer.
So, when someone says “The first integer square of integers is 0”, they are incorrect. With no lower bound, there is no such thing as a first integer, nor is there the square of a first integer.
You can say that “the smallest integer square of integers is 0” because any positive or negative integer squared will be greater than 0. One could also claim that “the first integer square of naturals is 0”, because the natural numbers (according to the formal definition) begin at zero, making zero the first natural number.
However - as already stated - it is impossible to define a “first” integer.
I’m just sayin’. There are others who think otherwise, and are willing to fight with tremendous conviction that integers have a lower bound. The particular disagreement that I am referencing is someone on Twitter bullying fans of the Layton experience based on that claim.
Also, I cannot help but wonder if the person doesn’t object because they thought that the Layton Twitter was the product of a big corporation, which the particular writer finds objectionable. Still. Sets of numbers aren’t open to debate.