What does "infinty as number" mean?
Dear Members,
What does the expression "infinity as number" mean to this 1788 group?
For better or worse, I had been under the impression it means the following three things:
1. Infinities are not members of the interval, although they may appear as endpoints of an interval to indicate an open (unbounded) endpoint.
2. To evaluate the difference (Inf-Inf) or ratio (Inf/Inf) of two infinities, the infinities are replaced with a real number x and then the arithmetic operation is considered in the limit as the magnitude x tends towards infinity. The same
is true for 0*Inf, which leads to 0*Inf=0.
3. Because of 2), Inf-Inf=0, Inf/Inf=1, and 0*Inf=0, but other arithmetic operations involving infinities are as usual, such as Inf+a=Inf for any real number a.
Did I abuse the terminology too much?
Sincerely,
Nate Hayes
Sunfish Studio, LLC