Zero Math Example 3

Follow the full solution, then compare it with the other examples linked below.

Example 3

easy
Is zero even or odd? Justify.

Solution

  1. 1
    An even integer is one that can be written as 2k2k for some integer kk.
  2. 2
    0=2×00 = 2 \times 0, so k=0k = 0 works.
  3. 3
    Therefore 0 is even.

Answer

0 is even0 \text{ is even}
The definition of even is n=2kn = 2k for integer kk. Since 0=2×00 = 2 \times 0, zero satisfies the definition. Zero is also consistent with the even-odd alternating pattern: …,−2,0,2,…\ldots, -2, 0, 2, \ldots

About Zero

The number representing the absence of quantity; the additive identity and placeholder in positional notation.

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More Zero Examples

Example 1 easy

Evaluate: (a) [formula], (b) [formula], (c) [formula].

Example 2 medium

Why is [formula] undefined? Explain using the definition of division.

Example 4 medium

The number [formula] has a zero in the tens place. How does removing that zero (writing 320 instead)

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