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Assumption: 1-1/x = 1 when x = infinity

Subtraction: -1/x = 0

Multiplication: -1 = 0x

Zero Property: -1 = 0

-1 does not equal 0, therefore 1-1/x does not equal 1 when x = infinity.

You cannot treat "infinity" like a normal number, you can only think of it in terms of limits.