| Title: | Mathematics at DEC |
| Moderator: | RUSURE::EDP |
| Created: | Mon Feb 03 1986 |
| Last Modified: | Fri Jun 06 1997 |
| Last Successful Update: | Fri Jun 06 1997 |
| Number of topics: | 2083 |
| Total number of notes: | 14613 |
Easy question:
For m, n integers, t real, what is the following category 2 function?
lim cos(pi*m*t)^(2*n)
m -> inf
n -> inf
- Jim
| T.R | Title | User | Personal Name | Date | Lines |
|---|---|---|---|---|---|
| 1085.1 | certainly bumpy | HERON::BUCHANAN | Andrew @vbo DTN 828-5805 | Mon Jun 05 1989 13:43 | 21 |
> For m, n integers, t real, what is the following category 2 function? > > lim cos(pi*m*t)^(2*n) = b(t) > m -> inf > n -> inf Define: l(t,m) = lim cos(pi*m*t)^(2*n) n -> inf This is 1 if m*t is an integer 0 otherwise If t is irrational, then b(t) exists and is zero. But if t is rational p/q, then l(t,m) has no limit, since l(t,m) has value 1 exactly when q | m. What does category 2 mean? Andrew. | |||||
| 1085.2 | AITG::DERAMO | Daniel V. {AITG,ZFC}:: D'Eramo | Mon Jun 05 1989 16:55 | 6 | |
I think the intention was to use m! instead of m in the argument to the cosine function. Then the limit for irrational t is zero, and the limit for rational t is one. That function is the "characteristic function" of the rationals. Dan | |||||