Question

What does this symbol mean?

Answer 1

\[N ^{*}\]

Answer 2

where N is the set of natural numbers

Answer 3

\[\mathbb{N} ^{*}\]

Answer 4

so that's N and then a *, star

Answer 5

zero is excluded from the set

Answer 6

a star denotes adjoint or sometimes the complex conjugate

Answer 7

A non-empty set X is an infinite set iff there exist an injection from \[\mathbb{N}^*\] to X

Answer 8

\[\mathbb N^*=\{1,2,3,...\}\]

Answer 9

so what is the difference with \[\mathbb{N} \quad\text{and}\quad \mathbb{N}^*\]

Answer 10

oh, zero is excluded. But are you sure about that? It seems weird to use that in a definition of infinite set instead of just N

Answer 11

Some people have different definitions for \(\mathbb N\)
to make sure you know which definition is being used
you can use these sub definitions

\[\large\mathbb N \sim\begin{cases} \mathbb N^0 =\{0,1,2,...\}\\ \mathbb N^*=\{1,2,3,...\}\end{cases}\]