What is the meaning of infinity?
There is no general definition that I know of that applies in all areas. It just means what it suggests to you intuitively, and has useful and specific implmentations in various topics such as limits, cardinal numbers in set theory etc.
dx is right. There is no single mathematical definition of "infinity"; there are lots of different concepts for different areas. You may refer to the "∞" of calculus, which is generally not treated as a number within calculus but can be identified with the "+∞" of the extended real numbers.
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