Yes and no. It's not a number in the traditional sense of a real or complex number. However, it is a number in the sense that it can be used to count and measure things.

If you can count it, it is not infinite. If you can measure it, it is not infinite. In certain cases, you can say you can do algebra with it, but it is neither physically countable nor physically measurable.

I agree completely that you can't "physically" count infinite things. You can, however, count infinite things in the sense of the mathematical theory of sets. The common example is the set natural numbers, which is countably infinite. (

http://mathworld.wolfram.com/CountablyInfinite.html)

Generally as used in physics, it is not a number, but a concept of making something arbitrarily large.

If that is how you are using the term infinity, then it is the wrong usage. Infinity is not a number that is arbitrarily large, it is a number that is provably uncountably large (i.e. if you believe it is a countable number, merely too large to be counted for practical reasons, then it is not infinity).

I have been very careful not to call infinity a number, since it isn't one. Number implies that it's contained in the set of natural numbers, which it isn't. It's a concept or quantity that is arbitrarily large. By arbitrarily large, I mean something that is larger than every real number. You can also define two types of infinities used in counting "countably infinite" (what you get if you count the natural numbers) or "uncountably infinite" (what you get if you count the real numbers). This is way beyond the scope of the question, but it shows you can use infinity to measure things.

In the sense of this question, though, infinity (or technically limit:x->infinity) pretty much describes the whole concept of the scientist sitting in a room constantly counting higher and higher...

You can prove that pi is an infinitely long number when expressed as a decimal value, but that is because you can show theoretically that you cannot ever possibly (not merely impractical to, but it is physically impossible to) count the total number of digits of pi in decimal notation.

Again, I agree completely that one cannot physically count to infinity. I never claimed anyone could. The idea of counting forever implies that you have infinite time in which to count, in which case if you sat down and chose any particular digit of pi, the counter would pass it eventually. In fact, this is an example of a countably infinite set, since you can arrange the decimal expansion of pi to map onto the natural numbers.

In the spirit of the original question, all this theory on infinity is probably way too detailed. There are three answers that pretty well sum up the question of trying to name the largest number:

(1) The largest number isn't well defined, since someone can come along and add 1 to anything you propose. (another_someone)

(2) The largest number we can represent is limited by the number of particles or amount of energy in the universe, since we'll run out of "stuff" to represent it with. (Soul Surfer)

(3) The largest quantity (though not a number) we can come up with is infinity.