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Proving a recursive definition by induction.
Define $lambda : {mathbb N} to {mathbb N}$ by $lambda(0) = 0$ and $lambda(n+1) = 1 + lambda(n)$, $n in mathbb N$.
Show by induction that $n geq 1 implies lambda(n) = n $.
Definition of $lambda(n)$ I would think was okay. The following seems to show it too, but I’m not sure.
$k=0$ $Rightarrow$ $lambda(0) = 0$ = $1 + 0$
$k=1$ $Rightarrow$ $lambda(1) = 1 + 0$
$k=2$ $Rightarrow$ $lambda(2) = 1 + 0$ and $lambda(1) = 1 + 1$ $Rightarrow$ $lambda(2) = 2 $
$k=3$ $Rightarrow$ $lambda(3) = 1 + 0 + 1$ and $lambda(1) = 1 + 1 + 1$
$vdots$
For the induction step, I’m not entirely sure. I feel like I have an answer but not completely sure.
$lambda(n+1) = 1 + lambda(n)$. So by induction,
$lambda(n+1) = 1 + 0$ and this makes sense by definition but is this how you show it?
A:
You’re almost there!
To start, for $n=0$, $lambda(1)=1+0=1$ and $lambda(0)=0$, both $lambda(0)=0$ and $lambda(1)=1$, so $lambda(0)=0$ and $lambda(1)=1$.
For $n=1$, $lambda(2)=1+1=2$. Since $lambda(0)=0$ and $lambda(1)=1$, $lambda(1)=1$ and $lambda(2)=2$. And so,
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All Activation Windows 7-8-10 v12 0 (Windows +Office Activator)Q:
Suggested edit on my own question that was declined
I posted this question a few months back. It was accepted by a few members and only minor editing was required.
The edit i made to my question was not accepted by anyone and later i got this message –
This suggested edit is incorrect or misleading.
I didnt know what to do so i added a comment.
I can understand it for the text that was inserted in my own question but it does not make sense for the code.
I searched for this exact issue on meta and found this.
But the edits made in that question were just typing the code and did not use the context of the question.
Did i do something wrong?
A:
Code is not part of your questions. It can only be part of answers.
If you fix your question to make it valid (which you should have done when you added the code in), then it will be accepted by the community (and it will then be by far the most useful contribution there).
If you just
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