Whole numbers property — The product of any number and the first whole number equals what fixed value? Clarify the definition of whole numbers.
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A1
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B2
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C3
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D0
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ESame as the number
Answer
Correct Answer: 0
Explanation
Introduction / Context:This question probes the definition of whole numbers and a basic multiplication property. Whole numbers typically start at 0 and include all non-negative integers: 0, 1, 2, 3, and so on. Knowing whether the sequence begins at 0 or 1 determines the result here.
Given Data / Assumptions:
- First whole number is 0.
- We consider an arbitrary real or integer n.
- Operation: product n * 0.
Concept / Approach:By definition of multiplication identity and zero property: 1 is the multiplicative identity (n * 1 = n), while 0 is the absorbing element (n * 0 = 0). Since the first whole number is 0, the product with any number will be 0.
Step-by-Step Solution:Identify first whole number = 0.Use zero property of multiplication: n * 0 = 0 for all n.Thus, the required product is 0.
Verification / Alternative check:Test examples: 7 * 0 = 0; 0 * 0 = 0; (-5) * 0 = 0. The result is always 0, confirming the absorbing property of zero under multiplication.
Why Other Options Are Wrong:
- 1 / 2 / 3: Confuse identity with zero; these are not universal products.
- Same as the number: That would be n * 1, not n * 0.
Common Pitfalls:Assuming the first whole number is 1; mixing up identity (1) with zero; overlooking that some texts say natural numbers start at 1 but whole numbers include 0.
Final Answer:0