Question

a fourth grader claims that \zero is nothing, so zero is neither even nor odd.\ whats your response?

choose the correct answer below.

a. zero is \something,\ namely, an especially important member of the whole-number system, and zero is an odd whole number.
b. zero is
othing,\ it does not belong to the whole-number system, but zero is an odd whole number.
c. zero is \something,\ namely, an especially important member of the whole-number system, and zero is an even whole number.
d. zero is
othing,\ it does not belong to the whole-number system, but zero is an even whole number.

Explanation:

Analyze the definition of even numbers

To address the claim, we must apply the mathematical definition of an even number. By the Even Number Definition, an integer \(n\) is even if it can be written in the form \(n = 2k\), where \(k\) is an integer.

Evaluate zero using the definition

We test if zero satisfies this definition:

$$0 = 2 \times 0$$

Since \(0\) is an integer, zero fits the definition perfectly. Therefore, zero is an even whole number.

Address the conceptual status of zero

Zero is not "nothing" in a mathematical sense; it is a well-defined number. It is "something," specifically a crucial member of the whole-number system that represents the quantity of nullity, acts as the additive identity, and possesses parity (evenness).

Match with the given options

We evaluate the choices:

• Option A incorrectly states zero is an odd whole number.
• Option B incorrectly states zero is "nothing" and is odd.
• Option C correctly states zero is "something," a member of the whole-number system, and is an even whole number.
• Option D incorrectly states zero does not belong to the whole-number system.

Answer:

• A. Zero is "something," namely, an especially important member of the whole-number system, and zero is an odd whole number.
• B. Zero is "nothing," it does not belong to the whole-number system, but zero is an odd whole number.
• C. Zero is "something," namely, an especially important member of the whole-number system, and zero is an even whole number. (Correct answer)
• D. Zero is "nothing," it does not belong to the whole-number system, but zero is an even whole number.