Quote:
Originally Posted by CraigS
Has the formalised mathematical definition of infinity, (ala Cantor, Godel,etc), ever resulted in productive outcomes for society ?
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At this stage no, but today's pure mathematics may become tomorrow's physics or applied mathematics.
An example of a mathematical theory of infinities which is used by theoretical physicists today is convergence testing of a series containing an infinite number of terms.
Even though a series may contain an infinite number of terms, it may converge to a finite value.
This is particularly important in solving certain partial differential equations used in physics and engineering. The "raw" series solution usually contains an infinite number of terms. If the series diverges it cannot be a solution to the equation.
Regards
Steven