Question 717054: Are there two numbers whose sum is greater then it's product
Answer by KMST(5328)   (Show Source):
You can put this solution on YOUR website! YES.
That is the short answer. It is a very open-response question. It can be expanded, elaborated, and various statements can be proven.
There are pairs of numbers whose sum is greater than their product and there are pairs for whom the product is greater.
If both numbers are equal or greater than 2, the product will be equal or greater than the sum, so do not look for examples there.
If we are talking about natural numbers (1, 2, 3, and so on), taking 1 as one of the numbers will always work, but otherwise you would have no solutions.
So the sets {1,1}, {1,2}, {1,3}, and so on work:
If we include zero and negative integers we can have more examples.
If we extend what we mean by "numbers" to rational, or real numbers we can have even more examples.
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