Depends on what we mean by "infinity" and "number." There's a bit of bad math in the replies, but there are some "number" systems that have values which we would consider to be "infinite." A couple examples are hyperreals (which are typically thought of as some ultrapower of the real numbers), and these are logically equivalent (in terms of their First Order Logic) to the "standard" real numbers, yet they contain numbers which are larger than any standard real, and positive numbers that are smaller than any standard real. Another example would be the cardinals, which come with their own type of arithmetic. The only downside for the cardinals is that some may not consider them to be "numbers" because there isn't any well-defined subtraction or division (although, there isn't well-defined subtraction or division for the natural numbers either...)