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I am having trouble understanding the concept of a limit not existing for functions like sin (1/x) when x tends to 0. The good book says that the function "does not settle on any value as we get closer to x" implying some infinite oscillation. I am having trouble visualizing it and why it should happen with this particular function.

Any kind soul here willing to elaborate on this and help me understand this better? I would be extremely grateful.

Many thanks,

Luca