-- How many
roads must a man walk down before he finds a
damn good pub?
Let us define n to be the number of roads a man must travel before he
finds the pub defined above. We may thus define n+1 to be the first
road which a man need not travel in order to reach a good pub. Now the
traversal of road n+1 is not a necessary condition, but rather a
sufficient one; thus it is sufficient for n+2 as well. Thus the
statement is true for x roads where x is >= n. Therefore, by induction,
it is true for any finite number x greater than n. We may conclude that
the statement is true for sufficiently large x, or alternatively that as
x approaches infinity, the number of roads that have been travelled
become sufficient to have found a good pub.
roads must a man walk down before he finds a
damn good pub?
Let us define n to be the number of roads a man must travel before he
finds the pub defined above. We may thus define n+1 to be the first
road which a man need not travel in order to reach a good pub. Now the
traversal of road n+1 is not a necessary condition, but rather a
sufficient one; thus it is sufficient for n+2 as well. Thus the
statement is true for x roads where x is >= n. Therefore, by induction,
it is true for any finite number x greater than n. We may conclude that
the statement is true for sufficiently large x, or alternatively that as
x approaches infinity, the number of roads that have been travelled
become sufficient to have found a good pub.
Related:
- HAKMEM /hak'mem/ n.
MIT AI Memo 239 (February 1972).
A legendary collection of neat mathematical and... - Productivity Equation
The productivity, P, of a group of people is:
P = N x T x (.55 - .00005 x N x (N - 1) ) where... - Proof techniques #1: Proof by Induction.
This technique is used on equations with "_n" in them.
Induction techniques are very popular, even the military... - Proof techniques #1: Proof by Induction.
This technique is used on equations with n in them.
Induction techniques are very popular, even the military... - Proof techniques #1: Proof by Induction.
This technique is used on equations with 'n' in them.
Induction techniques are very popular, even the military... - Proof techniques #1: Proof by Induction.
This technique is used on equations with "_n" in them.
Induction techniques are very popular, even the military... - define BITCOUNT(x) (((BX_(x)+(BX_(x)>>4)) & 0x0F0F0F0F) % 255)
#define BX_(x) ((x) -
(((x)>>1)&0x77777777) \ - (((x)>>2)&0x33333333)... - Lemma: All horses are the same color.
Proof (by induction):
Case n = 1: In a set with only one horse, it is obvious... - How many roads must a man walk down before you can
call him a cab...
