Mixing
Infinite descendant sequences
0
$begingroup$
"Show that the order $(A,<)$ is well ordering if and only if there no exists infinite descendant sequences in $A$".
Can you help me whit this problem, please, what happens is that my professor isn't gave us the definition of "infinite descendant sequences", so i haven't enough basis to solve this problem.
Thanks.
elementary-set-theory order-theory well-orders
asked Jan 18 at 23:14
Lennis MarianaLennis Mariana
255
$endgroup$
add a comment |
0
$begingroup$
"Show that the order $(A,<)$ is well ordering if and only if there no exists infinite descendant sequences in $A$".
Can you help me whit this problem, please, what happens is that my professor isn't gave us the definition of "infinite descendant sequences", so i haven't enough basis to solve this problem.
Thanks.
elementary-set-theory order-theory well-orders
asked Jan 18 at 23:14
Lennis MarianaLennis Mariana
255
$endgroup$
$begingroup$
can you specify your definition of well.ordering.
$endgroup$
– J.F
Jan 18 at 23:28
$begingroup$
A set $A$ is well ordering if all no-empty subset of $A$ have a minimum element.
$endgroup$
– Lennis Mariana
Jan 18 at 23:31
$begingroup$
A very standard equivalent one (which is i guess the thing you have to prove) is the following : Every decreasing sequence of elements of $A$ must be finite.
$endgroup$
– J.F
Jan 18 at 23:36
$begingroup$
Ok, i think i have the idea, i'll try to prove in this way, thanks.
$endgroup$
– Lennis Mariana
Jan 18 at 23:45
$begingroup$
I can put this as an answer to close the question if you want.
$endgroup$
– J.F
Jan 18 at 23:46
add a comment |
0
0
0
$begingroup$
"Show that the order $(A,<)$ is well ordering if and only if there no exists infinite descendant sequences in $A$".
Can you help me whit this problem, please, what happens is that my professor isn't gave us the definition of "infinite descendant sequences", so i haven't enough basis to solve this problem.
Thanks.
elementary-set-theory order-theory well-orders
asked Jan 18 at 23:14
Lennis MarianaLennis Mariana
255
$endgroup$
"Show that the order $(A,<)$ is well ordering if and only if there no exists infinite descendant sequences in $A$".
Can you help me whit this problem, please, what happens is that my professor isn't gave us the definition of "infinite descendant sequences", so i haven't enough basis to solve this problem.
Thanks.
elementary-set-theory order-theory well-orders
elementary-set-theory order-theory well-orders
asked Jan 18 at 23:14
Lennis MarianaLennis Mariana
255
asked Jan 18 at 23:14
Lennis MarianaLennis Mariana
255
edited Jan 18 at 23:32
Lennis Mariana
asked Jan 18 at 23:14
Lennis MarianaLennis Mariana
255
asked Jan 18 at 23:14
Lennis MarianaLennis Mariana
255
asked Jan 18 at 23:14
Lennis MarianaLennis Mariana
255
255
$begingroup$
can you specify your definition of well.ordering.
$endgroup$
– J.F
Jan 18 at 23:28
$begingroup$
A set $A$ is well ordering if all no-empty subset of $A$ have a minimum element.
$endgroup$
– Lennis Mariana
Jan 18 at 23:31
$begingroup$
A very standard equivalent one (which is i guess the thing you have to prove) is the following : Every decreasing sequence of elements of $A$ must be finite.
$endgroup$
– J.F
Jan 18 at 23:36
$begingroup$
Ok, i think i have the idea, i'll try to prove in this way, thanks.
$endgroup$
– Lennis Mariana
Jan 18 at 23:45
$begingroup$
I can put this as an answer to close the question if you want.
$endgroup$
– J.F
Jan 18 at 23:46
add a comment |
$begingroup$
can you specify your definition of well.ordering.
$endgroup$
– J.F
Jan 18 at 23:28
$begingroup$
A set $A$ is well ordering if all no-empty subset of $A$ have a minimum element.
$endgroup$
– Lennis Mariana
Jan 18 at 23:31
$begingroup$
A very standard equivalent one (which is i guess the thing you have to prove) is the following : Every decreasing sequence of elements of $A$ must be finite.
$endgroup$
– J.F
Jan 18 at 23:36
$begingroup$
Ok, i think i have the idea, i'll try to prove in this way, thanks.
$endgroup$
– Lennis Mariana
Jan 18 at 23:45
$begingroup$
I can put this as an answer to close the question if you want.
$endgroup$
– J.F
Jan 18 at 23:46
$begingroup$
can you specify your definition of well.ordering.
$endgroup$
– J.F
Jan 18 at 23:28
$begingroup$
can you specify your definition of well.ordering.
$endgroup$
– J.F
Jan 18 at 23:28
$begingroup$
A set $A$ is well ordering if all no-empty subset of $A$ have a minimum element.
$endgroup$
– Lennis Mariana
Jan 18 at 23:31
$begingroup$
A set $A$ is well ordering if all no-empty subset of $A$ have a minimum element.
$endgroup$
– Lennis Mariana
Jan 18 at 23:31
$begingroup$
A very standard equivalent one (which is i guess the thing you have to prove) is the following : Every decreasing sequence of elements of $A$ must be finite.
$endgroup$
– J.F
Jan 18 at 23:36
$begingroup$
A very standard equivalent one (which is i guess the thing you have to prove) is the following : Every decreasing sequence of elements of $A$ must be finite.
$endgroup$
– J.F
Jan 18 at 23:36
$begingroup$
Ok, i think i have the idea, i'll try to prove in this way, thanks.
$endgroup$
– Lennis Mariana
Jan 18 at 23:45
$begingroup$
Ok, i think i have the idea, i'll try to prove in this way, thanks.
$endgroup$
– Lennis Mariana
Jan 18 at 23:45
$begingroup$
I can put this as an answer to close the question if you want.
$endgroup$
– J.F
Jan 18 at 23:46
$begingroup$
I can put this as an answer to close the question if you want.
$endgroup$
– J.F
Jan 18 at 23:46
add a comment |
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$begingroup$
can you specify your definition of well.ordering.
$endgroup$
– J.F
Jan 18 at 23:28
$begingroup$
A set $A$ is well ordering if all no-empty subset of $A$ have a minimum element.
$endgroup$
– Lennis Mariana
Jan 18 at 23:31
$begingroup$
A very standard equivalent one (which is i guess the thing you have to prove) is the following : Every decreasing sequence of elements of $A$ must be finite.
$endgroup$
– J.F
Jan 18 at 23:36
$begingroup$
Ok, i think i have the idea, i'll try to prove in this way, thanks.
$endgroup$
– Lennis Mariana
Jan 18 at 23:45
$begingroup$
I can put this as an answer to close the question if you want.
$endgroup$
– J.F
Jan 18 at 23:46