Naturals without zero: { 1 , 2 , . . . } = N ∗ = N + = N 0 ∖ { 0 } = N 1 {\displaystyle \{1,2,...\}=\mathbb {N} ^{*}=\mathbb {N} ^{+}=\mathbb {N} _{0}\smallsetminus \{0\}=\mathbb {N} _{1}} Naturals with zero: { 0 , 1 , 2 , . . . } = N 0 = N 0 = N ∗ ∪ { 0 } {\displaystyle \;\{0,1,2,...\}=\mathbb {N} _{0}=\mathbb {N} ^{0}=\mathbb {N} ^{*}\cup \{0\}}