Post History
#3: Post edited
by
leovt
·
2021-08-14T13:38:32Z (about 3 years ago)
Tried to explain more clearly after feedback in the comment.
- If you set $k=0$ the equation becomes
- $$w_{0+1} - w_0 = r^{\textrm{exponent}}(w_1-w_0)$$
For this equation to hold (in general) the exponent must be $k=0$ and not $k+1=1$.- I think the problem is not a fence-post problem but the proper base case for the induction. Try to write down the step of going from
- $$w_{k+1} - w_k = r (w_k-w_{k-1})$$ to
- $$w_{k+1} - w_k = r^k (w_1-w_0)$$ as a proper proof by induction.
- If you set $k=0$ the equation becomes
- $$w_{0+1} - w_0 = r^{\textrm{exponent}}(w_1-w_0)$$
- For this equation to hold (in general) the exponent must be zero and not one. Thus an exponent of $k+1$ must be wrong.
- I think the problem is not a fence-post problem but the proper base case for the induction. Try to write down the step of going from
- $$w_{k+1} - w_k = r (w_k-w_{k-1})$$ to
- $$w_{k+1} - w_k = r^k (w_1-w_0)$$ as a proper proof by induction.
#2: Post edited
by
leovt
·
2021-08-11T16:55:28Z (about 3 years ago)
- If you set $k=0$ the equation becomes
- $$w_{0+1} - w_0 = r^{\textrm{exponent}}(w_1-w_0)$$
- For this equation to hold (in general) the exponent must be $k=0$ and not $k+1=1$.
- I think the problem is not a fence-post problem but the proper base case for the induction. Try to write down the step of going from
- $$w_{k+1} - w_k = r (w_k-w_{k-1})$$ to
$$w_{k+1} - w_0 = r^k (w_1-w_0)$$ as a proper proof by induction.
- If you set $k=0$ the equation becomes
- $$w_{0+1} - w_0 = r^{\textrm{exponent}}(w_1-w_0)$$
- For this equation to hold (in general) the exponent must be $k=0$ and not $k+1=1$.
- I think the problem is not a fence-post problem but the proper base case for the induction. Try to write down the step of going from
- $$w_{k+1} - w_k = r (w_k-w_{k-1})$$ to
- $$w_{k+1} - w_k = r^k (w_1-w_0)$$ as a proper proof by induction.
#1: Initial revision
by
leovt
·
2021-08-11T16:54:38Z (about 3 years ago)
If you set $k=0$ the equation becomes
$$w_{0+1} - w_0 = r^{\textrm{exponent}}(w_1-w_0)$$
For this equation to hold (in general) the exponent must be $k=0$ and not $k+1=1$.
I think the problem is not a fence-post problem but the proper base case for the induction. Try to write down the step of going from
$$w_{k+1} - w_k = r (w_k-w_{k-1})$$ to
$$w_{k+1} - w_0 = r^k (w_1-w_0)$$ as a proper proof by induction.