whats the largest rational number less than $\large \sqrt{2}$ ?

Question

inkyvoyd · Answer

hahaha very funny

inkyvoyd · Answer

(there isn't one)

rsadhvika · Answer

why, in the previous page it said rational numbers are ordered
so imm still a bit confused about whey there isn't one

inkyvoyd · Answer

here let me find a proof for you

inkyvoyd · Answer

This is taken from Rudin, principles of mathematical analysis

inkyvoyd · Answer

Let A be the set of all positive rational p such that p^2<2 and let B consist of all positive rational p such that p^2>2. We shall show that A contains no largest number and B contains no smallest.

inkyvoyd · Answer

omg it's scrambling my chats. Let me just take a picture fo ryou.

rsadhvika · Answer

okay i might be having a proof in my textbook too in later pages
 im still reading construction rational numbers.. but i want to see the proof as its really interesting xD

inkyvoyd · Answer

GL with real analysis.... I tried to get through it multiple times and it's just too dense

rsadhvika · Answer

they have constructed another greater rational number $\large q$ based on the given rational number $\large p$