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Consider 4 cases

1. The sum of any two positive numbers is clearly greater than either number.

2. The sum of any two negative numbers is LESS than either of the two numbers. ( (Look at -2+(-3)=-5 .)

3. The sum of any negative number and a positive number is always greater than the negative number but less than the positive number. (Look at -2+3=1, or -5+3=-2)

4. The sum of any number and 0 is that number so it is not greater.

So it appears that the sum of any two numbers is greater than either of the two numbers when the two number are both positive.

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Q: Is the sum of two numbers is always greater than either of the two numbers?
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