It was drilled into my head in school that it's not a proper limit unless it includes the text "lim A->B". So using infinity at all, without specifying that you're taking the limit, would be incorrect. This makes sense as infinity isn't a real number that you can actually be "equal to", just a concept you can approach, so you need to specify that by taking the limit, you're only approaching infinity. I guess the guy you're replying to needs to hear this more than you though.