"So formally, you can make such that the number infinity is included in the real line."
I can't say that you're wrong, but I can say truthfully that I don't follow the argument. (In particular, I'm not able to decipher "include into the real line ..."
I've read many scientific, mathematical, and (mostly) technical papers over the past 25 or so years that made use of infinity in one way or another. Not one has ever used infinity is as anything other than a transfinite number. In particular, none has ever used infinity as a real number.
I'm aware that some kinds of software (mathematica, for example) treat it as if it were a number. I always considered this to be a notational convenience. (It pretty much says exactly that on one of Wolfram's mathworld pages.)
The most dependable sites I can find on the web say that infinity is not a number. In fact, the only ones that I've found so far that maintain it IS a number are a newage site and an astrology site.
Do you have a reference that clearly expresses this idea? Doesn't necessarily have to be on the web.
