## ghazi Group Title 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? one year ago one year ago

1. ghazi Group Title

@carl_pham

2. henpen Group Title

Look up the principle of impotence

3. ghazi Group Title

i went through it and i am more nonplussed now

4. henpen Group Title

Although I admit I don't quite understand the question. Isn't defining a near-synonym for expression?

5. ghazi Group Title

no, i guess defining something is bit more general then deriving it and expressing it mathematically like we saw in the definition of force

6. henpen Group Title

So you worry that although force is intuitively obvious, there is no solid ground it safely rests on?

7. ghazi Group Title

yes, if you are defining something then it must satisfy every thing logically and mathematically too

8. Carl_Pham Group Title

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.

9. ghazi Group Title

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

10. woksman Group Title

Orange

11. Carl_Pham Group Title

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.

12. ghazi Group Title

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 ?

13. Carl_Pham Group Title

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).

14. ghazi Group Title

thanks, this is what, was hitting me.