We have to define what is meant by "infinity". Do you mean the infinity symbol one encounters in calculus with regard to limits? Do you mean infinite cardinal

We have to define what is meant by "infinity". Do you mean the infinity symbol one encounters in calculus with regard to limits? Do you mean infinite cardinal number? Infinite ordinal numbers? Do you mean the symbols added to the reals in order to compactify the set (extended real numbers)? Some other concept? Once that gets settled then we have to define what is meant by a number. I suggest that the most broad, reasonable definition of this concept would be elements of a ring. There should be some algebraic structure that is broad but not too broad. If we use such a definition then the various concepts of infinity mentioned above are not numbers since they are not elements of a ring. The limit example in the Wikibooks article is merely a shorthand notation and isn't a number. It's mostly to be suggestive and make things a bit easier to comprehend. It's not intended that a person think of it as a number.