Is it 0 is an even number?

As a domain expert in mathematics, I can provide a comprehensive explanation regarding the nature of zero as it pertains to the concept of even numbers. The question at hand is whether zero is considered an even number, and to answer this, we must delve into the definitions and properties that govern the classification of integers. Even Numbers and Their Definition: An even number is defined as an integer that can be expressed as a multiple of two. In mathematical terms, for any integer \( n \), if there exists an integer \( k \) such that \( n = 2k \), then \( n \) is even. This definition is fundamental and applies universally to all integers, including zero. Zero and the Definition of Even: When we consider zero in the context of this definition, we find that it indeed fits the criteria of being an even number. Since zero is the neutral element for addition, it can be considered a multiple of any non-zero integer. Specifically, if we let \( k = 0 \), then \( n = 2k \) becomes \( n = 2 \times 0 = 0 \). Thus, zero is an integer multiple of two, satisfying the condition for being even. **Historical Context and Mathematical Consensus:** Historically, there has been some debate over whether zero should be classified as even or odd. However, the modern mathematical consensus, as reflected in standard textbooks and mathematical literature, is that zero is indeed even. This consensus is based on the definition of even numbers and the properties that zero exhibits, which are consistent with those of other even numbers. Properties of Even Numbers: Even numbers have certain properties that zero also shares. For instance, the sum and product of two even numbers are always even. Since zero is even, it maintains these properties. When you add zero to any even number, the result is the even number itself, and when you multiply zero by any number, the result is zero, which is also even. Implications in Arithmetic and Algebra: Recognizing zero as an even number has implications for arithmetic and algebra. It ensures consistency in the application of rules and laws, such as the distributive property and the properties of exponents. For example, the statement \( a^0 = 1 \) for any non-zero \( a \) is a fundamental rule in algebra, and treating zero as even aligns with this rule. Conclusion: In conclusion, based on the definition of even numbers and the properties that zero exhibits, it is accurate to classify zero as an even number. This classification is supported by mathematical consensus and maintains consistency in mathematical operations and principles. References: 1. "Elementary Mathematics for Teachers" by Parker and Baldridge. 2. "Abstract Algebra" by David S. Dummit and Richard M. Foote. Now, let's proceed with the next steps as per your instructions.

Zero is an even number. In other words, its parity--the quality of an integer being even or odd--is even. This can be easily verified based on the definition of "even": it is an integer multiple of 2, specifically 0 -- 2.