If I have a stainless steel scale and bend it, it can undergo large deformation but will still come back to its original position. Now can I apply Hook's law for this large deformation?
Hooke's law can be applied in the elastic region of a material. Elastic region is defined the region in which the object can undergo deformation and return to original configuration in a reversible manner without loss of energy in the process. Steel is an elastic material .Thus yes. I can apply hooke's law here but not the small deformation theory. But for rubberbands we cannot apply hookes law because it is hyperelastic material and stress strain relation are not linear as in previous case.
What is the largest number you can represent which is not in the extended real number system(i mean not + or - infinity)
This is where the basic concept of limits needs attention. My answer to the above question would be "limit (epsilon ->0) 1/epsilon" here, epsilon is a real number and so is 1/epsilon. Now if you give me a huge real number, i can always make my epsilon smaller to give a bigger real number 1/epsilon. Note that i am still in real numbers and the number is not +or- infinity.. Clever right?! :)
How do you define mass?
The common answer most people give is "anything that has matter has mass". Few google results say "a coherent, typically large body of matter with no definite shape." or "We use the word mass to talk about how much matter there is in something. (Matter is anything you can touch physically.)" etc But this not a solid definition. The definition of mass comes from the concept of newton's laws. Especially the concept of "Inertia". Inertia is that property of a body which keeps the object from changing its state of motion unless external force is applied(Newtons first law). The more the inertia(The more resistance to change in state of motion) , the more the mass .One way of defining mass in terms of quantities we can measure is as follows "Mass is that property of matter which determines the acceleration of body when force is applied on it".(newtons second law) Now acceleration is a physical quantity measured as the rate of change of velocity which in turn is the rate of change of displacement, a basic quantity we can measure. The definition of force and mass thus may sound cyclic but is more quantitative than the definition of "amount of matter in a body"