What does this symbol denote in arithmetic, Z*?

Question

I know Z+, means all positive integers, but what does Z* means?

Answer 1

Have a look at this,

• Integers are denoted by Z, i.e. {. . ., -3, -2, -1, 0, 1, 2, 3, . . .}

• Z^+ denotes all positive integer sets i.e. {1, 2, 3, . . .} equivalent to N, Natural numbers.

• Z^- denotes all negative integer sets i.e. {-1, -2, -3, . . .} and

• Z^* denotes all non-negative integers, i.e. {0, 1, 2, 3, . . .}

For more information about arithmetic, go to Signed Numbers

Hope this clarifies!

Answer 2

Based on the OP's comment, I think the accepted answer is incorrect in this context. I think "$\mathbb{Z}_p$" is probably the ring of integers mod $p$ (also denoted "$\mathbb{Z}/p\mathbb{Z}$"), and $\mathbb{Z}_p^*$ is then the set of invertible elements of this ring. E.g. if $p=6$ then $\mathbb{Z}_p^*=\{[1], [5]\}$.

Note that really "$\mathbb{Z}_p$" shouldn't be used in this way - it conflates with the notation for the $p$-adic integers. But this is a common, if unfortunate, bit of notation.