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what is the difference between defining a quantity and expressing it, and how definition can be correlated with expression, also do they imply same meaning?

Physics
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Look up the principle of impotence
i went through it and i am more nonplussed now

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Other answers:

Although I admit I don't quite understand the question. Isn't defining a near-synonym for expression?
no, i guess defining something is bit more general then deriving it and expressing it mathematically like we saw in the definition of force
So you worry that although force is intuitively obvious, there is no solid ground it safely rests on?
yes, if you are defining something then it must satisfy every thing logically and mathematically too
An expression is an instance of a definition. The best illustration is the computer programmming assigment statement: i = i + 1 As an expression, this is stupid. As a definition, it makes perfect sense: i is now defined to be the previous value of i, plus 1.
so when we talk about force, it is anything that we push or pull (in classical mechanics) but when we use newtons second law we say \[F=\frac{ \Delta P }{ \Delta T }\] when there is no change in momentum there is no force but there could be force if we take example of force applied on body when there is no motion. this is why i am highly confused
Orange
Newton's Second Law is an equation of motion. It says how one measureable quantity (the momentum) changes, given some other measureable quantity (the force). From your point of view, it's an expression, not a definition.
when we talk about physics your example was a bit out of context though it is very obvious that if we won't define the variable we won't be able to run program, i just want to know in a general way, does mathematical expression always says or provides everything that is stated in the definition ?
Of course not. There are many situations where I could write the expression F = 0. That says nothing about whether in general, for that system, force is zero. As I said, an expression is an instance of a definition (or more than one definition, combined).
thanks, this is what, was hitting me.

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