Yes, they can be put into a one-to-one correspondence. The size of both sets is what's called a "countable infinity".
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The square of every positive or negative even whole number is a positive even whole number. The square of every positive or negative odd whole number is a positive odd whole number. There are an infinite number of each kind.
No. A mixed number is a whole number and a fraction.
An integer and a whole number are the same, by definition.
what whole number will 8 always divide by?
Just look at the last digit. If this is even, the whole number is even.