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







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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

















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







share|cite|improve this question
























  • 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















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







share|cite|improve this question















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






share|cite|improve this question















share|cite|improve this question













share|cite|improve this question




share|cite|improve this question








edited Nov 16 at 0:24

























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




















  • 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

















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