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Consider all pairs of natural numbers whose sum is less than 11. the two members of a pair could be either the same as each other or different. how many different products are possible if the two numbers are multiplied?

Respuesta :

There are infinite couples of numbers x and y such that x+y < 11, and thus there are infinite possible products of the two numbers.

Here's an example to generate infinite integers: fix [tex] x = 1 [/tex] and choose any value less than 10 for [tex] y [/tex].

So, you have

[tex] x+y = 1+y < 1+10 < 11 \ \text{and } xy = 1\cdot y = y [/tex]

So, for example, you may choose [tex] y = 0,1,2,3,4,5,6,7,8,9 [/tex] and have

[tex] x+y < 11 \ \text{and } xy = 0,1,2,3,4,5,6,7,8,9 [/tex]


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