Asking 'What is the smallest even number?' seems like a simple question for a primary school student, but the mathematical answer depends entirely on which set of numbers you are looking at (Natural, Whole, or Integers).
To easily prove that zero is even, look at the alternating pattern of integers on a number line: ... -3 (Odd), -2 (Even), -1 (Odd), 0 (Even), 1 (Odd), 2 (Even).
If we are only counting natural numbers (1, 2, 3, 4...), the smallest even number is 2. This is the answer most commonly taught in primary schools.
An even number is mathematically defined as any integer that can be divided by 2 without leaving a remainder.
Can 0 be divided by 2? Yes. (0 ÷ 2 = 0). Therefore, Zero (0) is an even number. If you are looking at the set of Whole Numbers (0, 1, 2, 3...), the smallest even number is 0.
If you include negative integers (... -4, -2, 0, 2, 4 ...), the numbers stretch towards negative infinity. Negative numbers like -2, -100, and -1,000,000 are also even numbers. Therefore, in the complete set of Integers, there is NO smallest even number, as it goes on endlessly into the negatives.
Just like even numbers, the smallest *positive* odd number is **1**. However, across all integers, there is no smallest odd number due to negative infinity.
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