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This is the name given to a "number" which is far larger than any number you can imagine. For example 1/x, when x is for all practical purposes, zero. Again, 1/infinity is zero. You cannot write out the value of infinity. For, twice it, the answer is infinity. It is used (implicitly) in calculus, for example, when doing integrals. The area under a curve representing a function on a graph can be found as a summation of lots of thin rectangles, whose width is small enough so that the height of each remains almost constant across the width. When you let the width go to "zero", you get an "infinite" number of rectangles and the summation sign is altered to that curvy "S" like symbol, and the width is represented by "dx", if the base coordinate is x. The area under the curve is finite and calculable, although the number of rectangles is effectively infinite. Another example is "the Sum to infinity" of some series, where the length of the series is infinite. An example is the sum (from n=0 to infinity) of all the terms x to the power n, divided by factorial n. (factorial n is the product of all integers 1 to n). This Sum is just e^x, or exponential of x. But you would never get there if you tried to do it simply by adding up all those terms!
An interesting question might be "is the universe finite?" First ask yourself "can I go on an infinite journey on the surface of the earth?" Yes you can, if you go on a spiral path starting at the north pole, with the distance between the spirals being infinitely small. So you might conclude erroneously that the surface of the earth is infinite, when it clearly is not.
answer 2. Infinity may be considered an arbitrarily large number. It is therefore uncountable, and beyond measure. It is best considered as a concept.
