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I was looking at the image of a piecewise continuous To understand the difference between continuity and uniform continuity, it is useful to think of a particular example of a function that's continuous on $\mathbb r$ but not uniformly continuous on $\mathbb r$. This might probably be classed as a soft question But i would be very interested to know the motivation behind the definition of an absolutely continuous function
To state a real valued function. Following is the formula to calculate continuous compounding a = p e^(rt) continuous compound interest formula where, p = principal amount (initial investment) r = annual interest rate (as a This is a general question A function is said to be continuous
Looking at the definition of continuity, i would say no Proving the inverse of a continuous function is also continuous ask question asked 11 years, 11 months ago modified 7 years, 10 months ago 3 this property is unrelated to the completeness of the domain or range, but instead only to the linear nature of the operator Yes, a linear operator (between normed spaces) is bounded if and only if it is continuous.
Basic real analysis should be a source of at least some intuition (which is misleading at times, granted) Can you think of some compact sets in $\mathbf r$ Are continuous functions on those sets uniformly continuous Can you remember any theorems regarding those
Continuous from the left/right ask question asked 4 years, 5 months ago modified 4 years, 5 months ago I know that the definition derives from calculus, but why do we define it like that?i mean what kind of property we want to preserve through continuous function?
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