MHB What is the concept of limiting event?

Thread starter WMDhamnekar
Start date Feb 20, 2022
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Concept

Feb 20, 2022

WMDhamnekar

MHB

Would any member of math help board prove highlighted 1 and 2 by simple and clear explanation with examples?

Last edited: Feb 20, 2022

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Aug 12, 2022

pbuk

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These are definitions, there is nothing to prove.

Aug 23, 2022

Stephen Tashi

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WMDhamnekar said:

with examples?

Try letting ##E_k## be the set defined by the open interval ##( 1 - \frac{1}{2^k} , 2 + \frac{1}{2^k})##

Thread 'Formal derivation of statement from Peano Arithmetic system'

I was reading a Bachelor thesis on Peano Arithmetic (PA). PA has the following axioms (not including the induction schema): $$\begin{align} & (A1) ~~~~ \forall x \neg (x + 1 = 0) \nonumber \\ & (A2) ~~~~ \forall xy (x + 1 =y + 1 \to x = y) \nonumber \\ & (A3) ~~~~ \forall x (x + 0 = x) \nonumber \\ & (A4) ~~~~ \forall xy (x + (y +1) = (x + y ) + 1) \nonumber \\ & (A5) ~~~~ \forall x (x \cdot 0 = 0) \nonumber \\ & (A6) ~~~~ \forall xy (x \cdot (y + 1) = (x \cdot y) + x) \nonumber...

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