Finding an injective (1-1) map into a smaller interval?
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As a side proof to a larger proof I am working on, I have to find an injective (1-1) map $Ato B$ where $A = (0,1) times (0,1)$ , $B= (0.5,0.6)$. How do you go about finding a a 1-1 map into a smaller interval like that.
real-analysis
asked Nov 15 at 23:33
Pablo Tores
124
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up vote
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down vote
favorite
As a side proof to a larger proof I am working on, I have to find an injective (1-1) map $Ato B$ where $A = (0,1) times (0,1)$ , $B= (0.5,0.6)$. How do you go about finding a a 1-1 map into a smaller interval like that.
real-analysis
asked Nov 15 at 23:33
Pablo Tores
124
Well, for example, the interval $(0,2)$ injects into the smaller interval $(0,frac 12)$ by $xmapsto frac x4$.
– lulu
Nov 15 at 23:34
1
math.stackexchange.com/questions/2290136/… will help you get an injection from $A$ to $(0,1)$. Can you get from $(0,1)$ to $B$, Pablo?
– Gerry Myerson
Nov 15 at 23:40
I understand when both start at 0 and when one of them isnt "x cross y".
– Pablo Tores
Nov 15 at 23:40
Gerry... I just need help finding an injective map between the A and B i gave
– Pablo Tores
Nov 15 at 23:45
1
It's just a composition of two maps. And you don't need to do it that way. It's just easier.
– Mason
Nov 16 at 2:42
|
show 3 more comments
up vote
0
down vote
favorite
up vote
0
down vote
favorite
As a side proof to a larger proof I am working on, I have to find an injective (1-1) map $Ato B$ where $A = (0,1) times (0,1)$ , $B= (0.5,0.6)$. How do you go about finding a a 1-1 map into a smaller interval like that.
real-analysis
asked Nov 15 at 23:33
Pablo Tores
124
As a side proof to a larger proof I am working on, I have to find an injective (1-1) map $Ato B$ where $A = (0,1) times (0,1)$ , $B= (0.5,0.6)$. How do you go about finding a a 1-1 map into a smaller interval like that.
real-analysis
real-analysis
asked Nov 15 at 23:33
Pablo Tores
124
asked Nov 15 at 23:33
Pablo Tores
124
edited Nov 16 at 0:24
asked Nov 15 at 23:33
Pablo Tores
124
asked Nov 15 at 23:33
Pablo Tores
124
asked Nov 15 at 23:33
Pablo Tores
124
124
Well, for example, the interval $(0,2)$ injects into the smaller interval $(0,frac 12)$ by $xmapsto frac x4$.
– lulu
Nov 15 at 23:34
1
math.stackexchange.com/questions/2290136/… will help you get an injection from $A$ to $(0,1)$. Can you get from $(0,1)$ to $B$, Pablo?
– Gerry Myerson
Nov 15 at 23:40
I understand when both start at 0 and when one of them isnt "x cross y".
– Pablo Tores
Nov 15 at 23:40
Gerry... I just need help finding an injective map between the A and B i gave
– Pablo Tores
Nov 15 at 23:45
1
It's just a composition of two maps. And you don't need to do it that way. It's just easier.
– Mason
Nov 16 at 2:42
|
show 3 more comments
Well, for example, the interval $(0,2)$ injects into the smaller interval $(0,frac 12)$ by $xmapsto frac x4$.
– lulu
Nov 15 at 23:34
1
math.stackexchange.com/questions/2290136/… will help you get an injection from $A$ to $(0,1)$. Can you get from $(0,1)$ to $B$, Pablo?
– Gerry Myerson
Nov 15 at 23:40
I understand when both start at 0 and when one of them isnt "x cross y".
– Pablo Tores
Nov 15 at 23:40
Gerry... I just need help finding an injective map between the A and B i gave
– Pablo Tores
Nov 15 at 23:45
1
It's just a composition of two maps. And you don't need to do it that way. It's just easier.
– Mason
Nov 16 at 2:42
Well, for example, the interval $(0,2)$ injects into the smaller interval $(0,frac 12)$ by $xmapsto frac x4$.
– lulu
Nov 15 at 23:34
Well, for example, the interval $(0,2)$ injects into the smaller interval $(0,frac 12)$ by $xmapsto frac x4$.
– lulu
Nov 15 at 23:34
1
1
math.stackexchange.com/questions/2290136/… will help you get an injection from $A$ to $(0,1)$. Can you get from $(0,1)$ to $B$, Pablo?
– Gerry Myerson
Nov 15 at 23:40
math.stackexchange.com/questions/2290136/… will help you get an injection from $A$ to $(0,1)$. Can you get from $(0,1)$ to $B$, Pablo?
– Gerry Myerson
Nov 15 at 23:40
I understand when both start at 0 and when one of them isnt "x cross y".
– Pablo Tores
Nov 15 at 23:40
I understand when both start at 0 and when one of them isnt "x cross y".
– Pablo Tores
Nov 15 at 23:40
Gerry... I just need help finding an injective map between the A and B i gave
– Pablo Tores
Nov 15 at 23:45
Gerry... I just need help finding an injective map between the A and B i gave
– Pablo Tores
Nov 15 at 23:45
1
1
It's just a composition of two maps. And you don't need to do it that way. It's just easier.
– Mason
Nov 16 at 2:42
It's just a composition of two maps. And you don't need to do it that way. It's just easier.
– Mason
Nov 16 at 2:42
|
show 3 more comments
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Well, for example, the interval $(0,2)$ injects into the smaller interval $(0,frac 12)$ by $xmapsto frac x4$.
– lulu
Nov 15 at 23:34
1
math.stackexchange.com/questions/2290136/… will help you get an injection from $A$ to $(0,1)$. Can you get from $(0,1)$ to $B$, Pablo?
– Gerry Myerson
Nov 15 at 23:40
I understand when both start at 0 and when one of them isnt "x cross y".
– Pablo Tores
Nov 15 at 23:40
Gerry... I just need help finding an injective map between the A and B i gave
– Pablo Tores
Nov 15 at 23:45
1
It's just a composition of two maps. And you don't need to do it that way. It's just easier.
– Mason
Nov 16 at 2:42