In a discussion on the SciMath forum a poster named Alan comments
I am reading through Elementary Real Analysis by Thomson, Bruckner & Bruckner. It is well-written, user friendly, and free!
His question just arises from the use of the word "continuous" and the discussion flows around how to sort it out. This is a quite normal process in learning a subject as subtle (I wouldn't say difficult) as real analysis. The nomenclature has a strange power to occlude your reasoning at first.
But I like the endorsement. I hope Alan will encourage us to quote him in all our promotions. Although it is an odd activity, to promote an entirely free product, there is some great reward in knowing that your users appreciate both the effort and the price.