On Sunday, October 1, 2017 at 2:08:13 PM UTC-6, John Gabriel wrote:
> [A] is an infinite series. > [B] is the limit of an infinite series.
> They are two different things which you are DEFINING to be the > same.
[A] might not be real. It might not really be something that makes sense.
[B], on the other hand, definitely does make sense, because each of the finite series in the sequence that approaches the limit certainly can be added up.
So what mathematicians are doing is saying, since [A] is bad, but we either would like to have [A], or we would like to refer to [B] by the name of [A] because it is shorter to skip mentioning that we're "really" talking about a limit, we will now say that whenever [A] is written, we will understand that [B] is what is really meant whenever it is necessary to concern oneself with that distinction.
This is not really such an awful thing for them to be doing.