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Apr
1
accepted (Graphics Gems IV, Shoemake) From matrix to euler angles explanation
Feb
19
comment What is the difference between a point and a vector
@Dr.Wily'sApprentice: no, in CG, points and vectors are not treated equally. They may be represented the same way though.
Dec
30
awarded  Popular Question
Mar
15
comment The Art of Computer Programming (2nd ed.): Mathematical Induction
Thanks a lot for all the explanations! It is much clearer now.
Mar
15
accepted The Art of Computer Programming (2nd ed.): Mathematical Induction
Mar
15
comment The Art of Computer Programming (2nd ed.): Mathematical Induction
let us continue this discussion in chat
Mar
15
comment The Art of Computer Programming (2nd ed.): Mathematical Induction
@arbautjc: this is exactly what I asked in my question actually. To use such an hypothesis P(1)..P(n) is true, I must prove it first. Right? And why n > 1 ? n > 0 is sufficient right?
Mar
15
comment The Art of Computer Programming (2nd ed.): Mathematical Induction
@arbautjc: no, based on my hypothesis that P(1)..P(n) is true, P(n+1) is also true. My hypothesis is wrong. That's why I believe that we should also prove P(1)..P(n).
Mar
15
awarded  Commentator
Mar
15
comment The Art of Computer Programming (2nd ed.): Mathematical Induction
@A.P.: so, I also have to prove P(1)..P(n) while proving P(n+1) => P(n). Right?
Mar
15
comment The Art of Computer Programming (2nd ed.): Mathematical Induction
@arbautjc: because we supposed that P(1)..P(n) is true. In particular, P(2) implies that a^1 = 1 and P(n) implies that a^(n-1) = 1.
Mar
15
comment The Art of Computer Programming (2nd ed.): Mathematical Induction
So what's wrong in: P(n): for all a, a^(n-1)=1. P(1): a^0, OK. Suppose P(1)..P(n) OK. P(n+1): a^((n+1)-1) = a^(n-1) x a^(1) = 1.
Mar
15
comment The Art of Computer Programming (2nd ed.): Mathematical Induction
Yes, but in complete induction, should you not prove P(1)...P(n) first?
Mar
15
comment The Art of Computer Programming (2nd ed.): Mathematical Induction
Yes, but in complete induction, should you not prove P(1)...P(n) first?
Mar
15
asked The Art of Computer Programming (2nd ed.): Mathematical Induction
Feb
27
awarded  Tumbleweed
Feb
23
revised (Graphics Gems IV, Shoemake) From matrix to euler angles explanation
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Feb
23
revised 3D Rotation Matrix Uniqueness
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Feb
3
awarded  Scholar
Feb
3
accepted 3D Rotation Matrix Uniqueness