A moment ago I saw the word affinity on a website, which jogged a memory from all the way back in grade 1 of primary/elementary school. The teacher had told us about infinity. Soon after, a female classmate (my only serious rival as the most advanced student in the class) drew a picture of a dancer with a large number of streamers, with the caption effinity streamers. I managed not to say anything to her, but I was inwardly scathing that she had misunderstood the concept and mis-spelled the word. Or maybe she hadn’t misunderstood: the first dictionary I checked just a moment ago includes the definition ‘indefinitely or exceedingly great’. There was certainly an exceedingly great number of streamers. (If I’d had to draw a picture illustrating infinity I would have drawn stars.)
Another definition is ‘
There doesn’t seem to be any difference in meaning (though mathematics may have specialised usages of limit-related words). In terms of the internet, Google Ngrams records unlimited internet from 1991 and unlimited broadband from 1992 (which may be a glitch in the data – the rate for 1993-1997 is identical) and limitless internet and limitless broadband not at all up to 2008 (when its data finishes).