Zero Element of Multiplication on Numbers
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Theorem
On all the number systems:
- natural numbers $\N$
- integers $\Z$
- rational numbers $\Q$
- real numbers $\R$
- complex numbers $\C$
the zero element of multiplication is zero ($0$).
Proof
This is demonstrated by showing that:
- $n \times 0 = 0 = 0 \times n$
for all $n$ in all standard number systems.
$\blacksquare$
Also see
Sources
- 1965: J.A. Green: Sets and Groups ... (previous) ... (next): $\S 4.3$. Units and zeros: Example $74$