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Earn +20 ptsQ: What is an even integer?
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What is the next even integer if n is an odd integer?
n + 1
Is there a greatest integer on the real number line?
No. For any integer, you can add one to get an even greater integer.
If 2n is an even integer what is the next even integer?
2n + 2 = 2(n+1)
What is the sum of the greatest even integer less than 2 and the smallest even integer greater than -1?
3
Why is the sum always odd when you add an even and an odd number?
An even integer is a multiple of 2 so that if x is the even integer then there is some other integer a such that x = 2a. An odd integer is one which, when you divide it by 2, leaves a remainder of 1. That is, if y is the odd integer, then y = 2b + 1 for some other integer b. Now, the sum of the even and odd integer is x + y = 2a + 2b + 1 = 2(a+b) + 1 By the closure of integers under addition, a and b are integers implies that a+b is an integer. So 2(a+b) is even and so the sum is odd.
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