Is dx=0 a correct statement?
No, if you mean "dx" here in the usual sense of a differential, it is NOT 0.
There are a number of different ways of interpreting "dx" depending on how you are handling Calculus itself. If you are using "Non-standard Analysis" (Calculus becomes very simple in "Non-standard Analysis" but it requires some very deep logic theory to show that it is valid), then "dx" and all differentials are "infinitesmals". If you use the more "standard" limit approach to Calculus, "dx" is purely a "symbol" that has no meaning by itself but can be connected to the ordinary derivative by "dy= f'(x)dx". In either case, it is not 0 (unless, of course, x itself represents a constant function).
(Hah! I finally beat someone by one minute!)
(Usually, I am the one who posts one or two minutes after another.)
The statement is meaningless. dx is not a number, but a symbol.
For integrals, it defines the integration variable.
For derivatives, it defines which function is being differentiated with respect to which variable.
If x is held constant, sure. We need context, are you taking a math class?
As the general answers say, the statement is rigorously meaningless unless used in very special (and typically advanced) scenarios. On an intuitive infinitesimal level, I'd say it means that ##x## is constant as algebrat says.
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