Infinity is the idea of something that has no end. In our world, we don't have anything like it. So we imagine traveling on and on, trying hard to get there, but that is not actually infinity. So don't think like that (it just hurts your brain!). Just think “endless”, or “boundless”, for instance. If there is no reason something should stop, then it is considered infinite.
Infinity is not “getting larger”, it is already fully formed. Sometimes people say it “goes on and on”, which sounds like it is growing somehow. But infinity does not DO anything, it just IS.
Infinity is not a real number. As aforementioned, it is an idea of something without an end. Infinity cannot be measured. Even faraway galaxies can't compete with infinity.
However, it is actually simpler than things which DO have an end. Because when something has an end, we have to define where that end is. A “Line” goes in both directions without end. When there is one end, it is called a “Ray”, and when there are two ends it is called a “Line Segment”, but they need extra information to define where the ends are. So a Line is actually simpler than a Ray or Line Segment. Even the sequence of natural numbers never ends, and is infinite. There are infinite points in a line, even the shortest line segment possible still has infinite points.
Yeah, I get the fact that 1/3 is a finite number, but written as a decimal number, the digit 3 repeats forever (we say “0.3 repeating”). There's no reason why the 3s should ever stop: they repeat infinitely. So, when we see a number like “0.999...” (i.e. a decimal number with an infinite series of 9s), there is no end to the number of 9s. You can not say "But what happens if it ends in an 8?", because it simply does not end. This is why 0.999... equals 1. Even an infinite series of "A"s followed by a "B" will NEVER have a "B".
In conclusion, infinity is just a simple idea: "endless". Most things we know have an end, but infinity does not. End 1000-word page essay.
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