If you've ever had an all-you-can-eat buffet for your meal, then you can probably realize how the notion of infinite demand of a product would be nonsense. Disregard the fact that in our economic system of today, you are paying a "one-time fee" each time. The point is that this is an example of a situation where a consumer has unlimited access to an available supply of a product - specifically, all kinds of food. There are several reasons you won't stay there until the restaurant closes for the day, for example you get full so you're no longer hungry, and there are other things you want to do besides eat non-stop all day.
That's just one example. There are actually plenty of other examples, including some that don't even involve paying anything. Imagine the first water fountain that comes to your mind, at the mall, the office building, school, a hospital, or wherever. Have you ever noticed the lack of endless lines of people with barrels waiting to fill them up to take advantage of the access to this free supply of water? I have. I wonder why? Just kidding; I don't. Same with restrooms; people can utilize them without paying for access to them, then leave when they're done taking care of business. How about an elevator as yet another example? Ever come across one that requires you to insert a quarter before the doors will open or you can select your floor? Perhaps there is one out there like that somewhere, but I've never come across one. There are also things like libraries, TV, radio, and the Web that also allow access without fees (other than ISP, electric bill, one-time purchase of devices, etc.) to things like information, entertainment, and software.
The reason that there would seem to be an infinite demand to an available supply of something is because there is an infinite demand for money. The problem is that money (in the abstract sense) is not actually an available supply of any kind of product. Here's why: imagine you're offered a check made out for the amount of $500 million (a real one, not one that's going to bounce), but in exchange for it you're told by the person writing out that check that you have to be stranded on a desert island, you can't tell anyone where you'll being taken, you may not give that money to someone else, and you may not bring any kind of communication device before you'll receive the check. Imagine what you can do stranded on a desert island with a check for $500 million. Not much of anything, right?
Even if you were allowed to go to a bank to cash in your $500 million and bring it with you before being dropped off on the deserted island, what use would that pile of cash be to you? Well, actually there is something you might be able to use it for, such as building shelter or making blankets (let's just say that the person who wrote you the check gave you a needle and adequate supply of thread, etc. to help you make these things). But in that case you're actually using the physical medium for money to physically construct something out of this cash, and it has nothing to do with the value or denomination printed on them; in other words, you could just use the same material used to make the cash without it being currency to do the same thing.