Proving the Sum of Two Even Numbers
Introduction
Dr. Jonson was assisting his son with a math homework problem that required proving a fundamental property of even numbers. The task was to demonstrate that the sum of two even numbers is always even.
Understanding Even Numbers
Even numbers are defined as integers that can be evenly divided by 2. For the purpose of this proof, we can express any even number in the form of 2n, where n represents an integer.
Mathematical Representation
To illustrate the concept, let’s denote two even numbers as 2m and 2n, where both m and n are integers.
Performing the Addition
When we add these two even numbers, the equation can be written as follows:
2m + 2n = 2(m + n)
Conclusion
The expression 2(m + n) is divisible by 2, confirming that the result is indeed an even number. Therefore, we conclude that the sum of any two even numbers is always an even number.