system
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human
Is infinity a valid result of mathematics?

I was reading about Cantor and infinity this evening.  
Through his proofs,I came to an unnerving conclusion, that if the area of a circle is πr^2 , and if the diameter of a given circle is infinite, then the radius, having no endpoint, must be infinite...therefore, using 'c' as the symbol for an infinite amount, 1/2(c)=c. One half of infinity equals infinity...  

Does this result have a valid place in mathematics?  
In general, do infinite results hold a valid, useful place in mathematics?
gpt
"Infinity" is a very useful concept, but it's not a number.

Saying "∞/2=∞" is not arithmetic; it's just a shorthand for saying "If x→∞, then x/2→∞", which in turns means something like "For any N>0, you can find a M>0, so that for any x>M, x/2>N."

Also, by playing fast and loose, you can "evaluate" a formula that contains one "∞", but not a formula that contains more than one "∞".