Question

y pi iz an irrational number?

Answer 1

it cannot be written as a fraction p/q where p and q are integers

Answer 2

cause it never ends. there are an infinite number of decimal places

Answer 3

pi -irational

Answer 4

the proof is quite complex i think

Answer 5

thanx dearz

Answer 6

not really

Answer 7

its not just because "it never ends" , 1/3 is rational and "it never ends"

irrational number have no repeating pattern

Answer 8

whant the proof?

Answer 9

well i mean relative to the proof that square root of 2 is irrational

if you want to supply the proof go ahead :)

Answer 10

k, here it comes...

Answer 11

give proof plz.

Answer 12

jreis plz introduced urcelf?

Answer 13

supose the oposit:
\[\sqrt{2}= p/q\] where p, q are natural numbers. In this case:
\[(p/q)^{2} =2\] We can asume that p, and q are the simpliest fraction (ireductible). But:
\[p ^{2} = 2*q ^{2}\] It mens p is an even number p= 2r for some natural r. And consecuently q is an odd number (remember ireductible fraction). Put in place of p it's expretion 2r and oyu get:\[(2r)^{2} = 2q ^{2}\rightarrow q ^{2} = 2r ^{2}\] It folows from here that q is even. We get contradiction which proves that sqrt(2) is irational.

Answer 14

\[\pi \ne \sqrt{2}\]

Answer 15

lol

Answer 16

the proofs i've seen dont seem very simple, they all rely at least on some integration -
http://en.wikipedia.org/wiki/Proof_that_%CF%80_is_irrational

Answer 17

i like the continued fraction one though

Answer 18

@eigenschmeigen asked for sqrt(2)

Answer 19

dont think i did xD although that was a perfect proof that sqrt(2) is irrational

Answer 20

eigenschmeigen

2
Good Answer


well i mean relative to the proof that square root of 2 is irrational

if you want to supply the proof go ahead :)

Answer 21

lol ... looks like myko got the same problem as me.

Answer 22

yes , i was comparing the difficult proof of pi's irrationality to the simpler proof of sqrt(2)

Answer 23

kk, didn't read the hall thing, my bad

Answer 24

no worries :)

Answer 25

heres a nice one: "prove that if k is rational, k + sqrt(2) is irrational"

Answer 26

thats quite simple .. more general would be rational + irrational = irrational

Answer 27

maybe:

prove that there is always at least 1 irrational between two rationals

Answer 28

quite a daunting question

Answer 29

there is a real nice solution though

Answer 30

not in a mood to solve it. i would appreciate if you would post here!!

Answer 31

:D

Answer 32

i know you can always construct irrational number between two numbers, but proving numerically would seem special case.

Answer 33

let
\[x \text{ , }y \in \mathbb{Q} : x<y\]

now \[x< x +\frac{1}{\sqrt{2} }(y-x) <y\]
and now you just have to prove

\[\frac{1}{\sqrt{2} }(y-x) \]

is irrational

assume that its rational (of form p/q)

and we get

\[\frac{q(y-x)}{p }=\sqrt{2} \]

which is a contradiction as the square root of 2 is irrational

Answer 34

its basically constructing one algebraically

Answer 35

i like it though

Answer 36

nice and easy ... i like it