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Large numbers hard to comprehend such as google, googleplex, graham's number and infinity and their significance in mathematics. The infinite room hotel is used to conceptualize infinitely.
Infinity comes in different sizes which can be shown mathematically.
The finite size universe versus infinite size universe theory.
The infinite monkey theorem and Shakespeare. How long would it take a monkey to write Shakespeare?
Cosmic inflation theory explains the cosmic background radiation and if it is correct an infinitely expanding universe is implied. Infinitely expanding universe may also mean there are (infinite) multi-universes. In infinite universes anything happens all the time as can be different laws of physics for these other universes.