[Koshkin]

To be fair, you can have a field that only has integers. For example, Z mod 5 is a field.

[carloswilson]

I am aware. It is typically represented as Z_5. They are called prime fields.

I highly doubt wsxcde meant prime fields in their comment though. wsxcde seemed to be talking about the set of all integers and the set of all real numbers in their comment. Only the latter is a field (and a ring) whereas the former is only a ring.

And (-a)(-b) = ab holds in rings (and thus fields).