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- finance - Proof of Continuous compounding formula - Mathematics Stack . . .
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 decimal) t = number of years A = amount after time t The above is specific to continuous compounding
- Difference between continuity and uniform continuity
I understand the geometric differences between continuity and uniform continuity, but I don't quite see how the differences between those two are apparent from their definitions For example, my book
- general topology - Closure of continuous image of closure - Mathematics . . .
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- probability theory - Why does a C. D. F need to be right-continuous . . .
This fact is useful to resolve this natural question: Let $\{X_i\}_{i=1}^{\infty}$ be i i d random variables uniform over $[-1,1]$
- is bounded linear operator necessarily continuous?
Added @Dimitris's answer prompted me to mention, beyond the fact that the implication on normed spaces indeed is an equivalence, that it's the converse which holds in the wider context of topological vector spaces, while the proposition mentioned here fails: there are bounded discontinuous linear operators, yet every continuous operator remains
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