Archive for January 17th, 2008

From Infinity to Divinity

January 17, 2008

There was a young fellow from Trinity (Cambridge University?)…..
…..Who took √∞ ….. But the number of digits….. Gave him the fidgets…..
He dropped Math and took up Divinity…
Hehehehe … ∞
This is the phrase at the bottom of title page of the book One, Two, Three…Infinity by George Gamow.
I enjoyed reading it, since it is about facts [...]

Some Proofs on Irrationality

January 17, 2008

Prove that √5 + √3 is irrational
(No.4 of Problem Set 10 in Numbers: Rational and Irrational by Ivan Niven)
Solution:
The argument made here is a proof by contradiction or reductio ad absurdum; That is, assuming that the proposition is false and then derive a contradiction from this assumption.
Note: My solutions are also parallel to Prof. Niven’s
First, [...]