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Can I use inductive proof on set of infinite sequences?
Assume $a$ is an infinite sequence. $a(i)models p$ means the $i$th index of $a$ satisfies the $p$ property.
Given that $a(0)models p$ and $forall i. iinmathbb N land a(i)models p implies a(i+1)models p$. Can I use inductive proof to prove that ${amid forall i.iinmathbb N implies a(i)models p}neq emptyset$?
The problem here is that $a$ is an infinite sequence while the $i$ is a nature number.
sequences-and-series
asked Nov 20 '18 at 12:05
Gabriel
1012
add a comment |
Assume $a$ is an infinite sequence. $a(i)models p$ means the $i$th index of $a$ satisfies the $p$ property.
Given that $a(0)models p$ and $forall i. iinmathbb N land a(i)models p implies a(i+1)models p$. Can I use inductive proof to prove that ${amid forall i.iinmathbb N implies a(i)models p}neq emptyset$?
The problem here is that $a$ is an infinite sequence while the $i$ is a nature number.
sequences-and-series
asked Nov 20 '18 at 12:05
Gabriel
1012
What are infinite traces?
– Asaf Karagila♦
Nov 20 '18 at 12:08
infinite traces can be seen as infinite sequences
– Gabriel
Nov 20 '18 at 12:13
add a comment |
Assume $a$ is an infinite sequence. $a(i)models p$ means the $i$th index of $a$ satisfies the $p$ property.
Given that $a(0)models p$ and $forall i. iinmathbb N land a(i)models p implies a(i+1)models p$. Can I use inductive proof to prove that ${amid forall i.iinmathbb N implies a(i)models p}neq emptyset$?
The problem here is that $a$ is an infinite sequence while the $i$ is a nature number.
sequences-and-series
asked Nov 20 '18 at 12:05
Gabriel
1012
Assume $a$ is an infinite sequence. $a(i)models p$ means the $i$th index of $a$ satisfies the $p$ property.
Given that $a(0)models p$ and $forall i. iinmathbb N land a(i)models p implies a(i+1)models p$. Can I use inductive proof to prove that ${amid forall i.iinmathbb N implies a(i)models p}neq emptyset$?
The problem here is that $a$ is an infinite sequence while the $i$ is a nature number.
sequences-and-series
sequences-and-series
asked Nov 20 '18 at 12:05
Gabriel
1012
asked Nov 20 '18 at 12:05
Gabriel
1012
edited Nov 20 '18 at 12:12
asked Nov 20 '18 at 12:05
Gabriel
1012
asked Nov 20 '18 at 12:05
Gabriel
1012
asked Nov 20 '18 at 12:05
Gabriel
1012
1012
What are infinite traces?
– Asaf Karagila♦
Nov 20 '18 at 12:08
infinite traces can be seen as infinite sequences
– Gabriel
Nov 20 '18 at 12:13
add a comment |
What are infinite traces?
– Asaf Karagila♦
Nov 20 '18 at 12:08
infinite traces can be seen as infinite sequences
– Gabriel
Nov 20 '18 at 12:13
What are infinite traces?
– Asaf Karagila♦
Nov 20 '18 at 12:08
What are infinite traces?
– Asaf Karagila♦
Nov 20 '18 at 12:08
infinite traces can be seen as infinite sequences
– Gabriel
Nov 20 '18 at 12:13
infinite traces can be seen as infinite sequences
– Gabriel
Nov 20 '18 at 12:13
add a comment |
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What are infinite traces?
– Asaf Karagila♦
Nov 20 '18 at 12:08
infinite traces can be seen as infinite sequences
– Gabriel
Nov 20 '18 at 12:13