Continuity vs Differentiability
The cluster focuses on debates about properties of mathematical functions, particularly distinguishing continuity from differentiability, analytic functions, polynomial approximations, integrals, and derivatives like the exponential function.
Activity Over Time
Top Contributors
Keywords
Sample Comments
Hey, I feel you, my first thought was that continuously differentiable functions aren't physical :)
What if you're not approximating a continuous function?
Agreed, functions should be continuous and no step functions.
Does this also hold for other functions such as sin, asin, multiplication, division, etc?
Why is f(x) = 1 + integral_0^x f(x)?
It would seem that you mean "continuous" here, instead of "differentiable".
Continuous functions aren't necessarily differentiable.
and if it's not a continuous function?
Go on then, explain this nondifferentiable constant case I was missing.
Do you mean something other than the sense the author mentions, that it can't be given in terms of elementary functions?