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The Difference between 0 and Meaningless in Mathematics
A value of 0 indicates that the value has a specific meaning and the size is 0.

Meaningless means that this value has no specific meaning, so it has no size.

For example, for the function y= 1- 1/x,

When x= 1 and y=0, we understand that the function value is 0 (that is, the value of 0 is the expression of the concept of size).

When x=0, 1/x is meaningless. At this time, y has no value, that is, the function value does not exist (meaningless is a formula that cannot be calculated or violates mathematical common sense)