# Zero

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Zero, or $0$, is the smallest ordinal and cardinal number. It is usually represented by the empty set, denoted $\varnothing$ or $\{\}$.
Given an ordinal (or cardinal) $x$:
• $x + 0 = 0 + x = x$.
• $x \cdot 0 = 0 \cdot x = 0$
• $x^0 = 1$
• $0^x = 0$ if $x > 0$