Question

plz help me and i will give you medel
explain red under lines

Answer 1

What is the question

Answer 2

Like what is an example?

Answer 3

Please be more specific.

Answer 4

ok so what you want is

Answer 5

3rd and 4th line " if t = x/1+x then then 0<t<1 then t^n<t<x hence E is not empty and next step if t>1+x then....... this part is confuding me first question is why he choose t = x/1+x and secong question is in 3rd line he said t^n< t<x means (t<x)but in 4th line he write "t>1+x" how its possible?

Answer 6

i want to know what writer (rudin) did and how he did?

Answer 7

the answer to "why he chose it" is obscure, probably because this is what makes the proof work

Answer 8

actually it is not that obscure
the first step is to show that E is not empty, E being the set of all numbers \(t\) such that \(t^n<x\)

Answer 9

@satellite73 i wana answer of my second question look at 3rd and 4th line in 3rd line t<x but in 4th line t>1+x how he did ?

Answer 10

let me look carefully

Answer 11

actually now i am confused
he says if \(t>1+x\) then \(t^n>1>x\) but i am confused as to why \(1>x\)

Answer 12

do it carefully @satellite73 i m working on this problem since few days. i didnt get any help from google or youtube .....

Answer 13

ooh no duh i read it wrong sorry

Answer 14

it says if \(t>1+x\) then \(t^n>t>x\) and that is pretty clear

Answer 15

i it pretty obvious that if \(t>1+x\) then \(t>x\) right?

Answer 16

yes this is 4th line but in 3rd line he said \[t^{n}<t <x\] 3rd and 4rh line are opposite to each other

Answer 17

they are two separate cases
there is an IF between them

Answer 18

IF \(t=\frac{x}{1+x}\) then blah blah so E is not empty
IF \(t>1+x\) then blah blah so \(t\) is not in E so \(1+x\)is a upper bound

Answer 19

yes i know two different cases but in first case he already proved that t<x then how he take t>1+x?

Answer 20

IIIIFFFFF

Answer 21

look lets do it with a number and see what it means

Answer 22

lets show that there is a number in the set E, where E is the set of numbers \(t\) for which \(t^2<3\)

Answer 23

x is also upper bond becoz x is greater then t and also t^n then why he felt to take 1+x

Answer 24

if \(t=\frac{3}{4}\) then \(t^2<1<3\) so E is not empty
If \(t>1+3=4\) then \(t^2>t>3\) i.e. \(4^2>4>3\) so \(4\) is not in E

Answer 25

oh i think i can explain that

Answer 26

suppose \(t=\frac{1}{3}\) then it is not true that \(t^n>t\)

Answer 27

to prove upper bound which theorem or property he used?

Answer 28

he showed that \(1+x\) is an upper bound for E, i.e. that if \(t=1+x\) then \((1+x)^n>x^n\) so \(1+x\) is n upper bound for E

Answer 29

how he proved? using any contradiction of case one ?