Example of Order isomorphism in well order set
Sir there is a theorem which says "let (X, <)and (X',<) be wosets. If they are order isomorphic to each other there is exactly one isomorphism exists "and there is an example saying that well order is essential. In a totally order set it violates by giving example f from Z to Z defined by fm( n)=m+n. Sir my doubt is, does this violets in N also??? As N is a woset,if m not equal to m' fm not equal to equal to fm' is holding there also.
order-theory
asked Nov 29 at 0:01
Resmi
1
add a comment |
Sir there is a theorem which says "let (X, <)and (X',<) be wosets. If they are order isomorphic to each other there is exactly one isomorphism exists "and there is an example saying that well order is essential. In a totally order set it violates by giving example f from Z to Z defined by fm( n)=m+n. Sir my doubt is, does this violets in N also??? As N is a woset,if m not equal to m' fm not equal to equal to fm' is holding there also.
order-theory
asked Nov 29 at 0:01
Resmi
1
3
The function $f_1:mathbb Ntomathbb N$ defined by $f_1(n)=n+1$ is order-preserving and injective, but not surjective, so it's not an isomorphism.
– bof
Nov 29 at 0:06
add a comment |
Sir there is a theorem which says "let (X, <)and (X',<) be wosets. If they are order isomorphic to each other there is exactly one isomorphism exists "and there is an example saying that well order is essential. In a totally order set it violates by giving example f from Z to Z defined by fm( n)=m+n. Sir my doubt is, does this violets in N also??? As N is a woset,if m not equal to m' fm not equal to equal to fm' is holding there also.
order-theory
asked Nov 29 at 0:01
Resmi
1
Sir there is a theorem which says "let (X, <)and (X',<) be wosets. If they are order isomorphic to each other there is exactly one isomorphism exists "and there is an example saying that well order is essential. In a totally order set it violates by giving example f from Z to Z defined by fm( n)=m+n. Sir my doubt is, does this violets in N also??? As N is a woset,if m not equal to m' fm not equal to equal to fm' is holding there also.
order-theory
order-theory
asked Nov 29 at 0:01
Resmi
1
asked Nov 29 at 0:01
Resmi
1
asked Nov 29 at 0:01
Resmi
1
asked Nov 29 at 0:01
Resmi
1
asked Nov 29 at 0:01
Resmi
1
1
3
The function $f_1:mathbb Ntomathbb N$ defined by $f_1(n)=n+1$ is order-preserving and injective, but not surjective, so it's not an isomorphism.
– bof
Nov 29 at 0:06
add a comment |
3
The function $f_1:mathbb Ntomathbb N$ defined by $f_1(n)=n+1$ is order-preserving and injective, but not surjective, so it's not an isomorphism.
– bof
Nov 29 at 0:06
3
3
The function $f_1:mathbb Ntomathbb N$ defined by $f_1(n)=n+1$ is order-preserving and injective, but not surjective, so it's not an isomorphism.
– bof
Nov 29 at 0:06
The function $f_1:mathbb Ntomathbb N$ defined by $f_1(n)=n+1$ is order-preserving and injective, but not surjective, so it's not an isomorphism.
– bof
Nov 29 at 0:06
add a comment |
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The function $f_1:mathbb Ntomathbb N$ defined by $f_1(n)=n+1$ is order-preserving and injective, but not surjective, so it's not an isomorphism.
– bof
Nov 29 at 0:06