1 let S be a set and assume that 0 noequal to S suppose that

1. let S be a set and assume that 0 noequal to S. suppose that sup S= M. Define S EXPONENT r = {1/x\\x belong to S}. prove that infSexponent r = 1/M.

2. a triangle of integers is an arrangement of three integers in a triangle. for example: 2         and 7             are two

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different triangle of integers. prove that T is denumerable. thanks

Solution

1.

S is a set

S not equal to 0

sup S = M

--> M is the largest value in the set S

S exponent=r = {(1/x) | x belongs to S }

When x is maximum ,(1/x) has the least value

so S exponent has the least value when x = sup S = M

inf (S-exponent) = (1/M)

2.

The question is not complete