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Proving that an equality is false.

I have two sets of 64 numbers (1.1 to 7.4). Both number sets are created using the same equation for values of i from 0 to 63.

m = 1.1 + ( i * 0.1 )

n = 1.1 + ( i * 0.1 )

I am trying to understand if the following equality is false in all cases except when the terms in each expression are equal (e.g. m^-12 = n^-12 and so on).

m^-12 + m^-11 + m^-10 + m^-9 + m^-8 + m^-7 + m^-6 + m^-5 + m^-4 + m^-3 + m^-2 = n^-12 + n^-11 + n^-10 + n^-9 + n^-8 + n^-7 + n^-6 + n^-5 + n^-4 + n^-3 + n^-2

There are no restrictions regarding utilization of the numbers in the number sets: the same number may be used repeatedly in the expression (e.g. 0.1^-12 + 0.1^-12 and so on).

Alternatively, I need to identify when the equality will be true in cases where the terms are different (e.g. m^-12 not equal to n^-12 and so on).

Solution Summary

An equality is proven to be false. The solution is detailed and well presented.

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