What does the ^ symbol mean in a math problem like 8x^3 - 4x? How do you write a Mathematics question? What is the difference between the symbols / and %? How do you describe a partition in math? How do you write formal proofs in math?
21 September, 2013 in expository, math.CO, math.NT | Tags: Dickman's function, permutations, point processes, Poisson-Dirichlet process, prime numbers | by Terence Tao | 29 comments Define a partition of to be a finite or infinite multiset of real numbers in the interval (that is, an...
Theorem 1 resembles other theorems in density Ramsey theory, such as Szemerédi’s theorem, but with the notable difference that the pattern located in the dense set is infinite rather than merely arbitrarily large but finite. As such, it does not seem that this theorem can be proven by purel...
While the ball does indeed bounce an infinite number of times, with the bounces getting smaller and smaller in height, that doesn’t mean it keeps bouncing forever. The bounces get smaller and smaller not only in height, but also in duration, and the sum of their durations converges to a...
Note the soldering on the crystal’s load capacitors C9 and C10 in the photo below, part of an attempt to find the optimum load capacitance on a prototype board. All of these issues mean that just assembling the PCB and hoping for the best doesn’t work well. The frequency of an ...
SPM Storage Partition Manager SPM Seat-back Processor Module SPM Super Memoratus (Latin: Mentioned Above; codices and manuscripts) SPM Static Propagation Mechanism SPM System Performance Model/Modeling SPM Sua Propria Manu (written in place of address on personally delivered envelopes) SPM Switch Power...
It probably couldn’t be as low as 60 or as high as 80, but no one would beshockedif it turned out to be 68 km/s/Mpc, or maybe as high as 74 km/s/Mpc. This could mean a Universe as old as maybe 14.2 billion years, or as young as 13.3 billion years, depending on how...
In this short note I would like to use the mean ergodic theorem to show that ergodic systems also have the property that “somewhat locally constant” functions are necessarily “somewhat globally constant”; this is not a deep observation, and probably already in the literature, but I found ...
I do not have proofs of these results (though I think something similar to (i) can be found in Knapp’s book, and (ii) should basically follow by using a rational parameterisation of with nonlinear). Assuming these assertions, this would mean that there is a curve of the form that ca...
Needless to say, this program turns out to be far more difficult than the above summary suggests, and the actual proof of the CFSG does not quite proceed along these lines. However, a significant portion of the argument is based on a generalisation of this strategy, in which the concept ...