19 December, 2024 in expository, math.MG | Tags: cosmic distance ladder, quaternions, spherical trigonometry | by Terence Tao | 11 comments Hamilton’s quaternion number system is a non-commutative extension of the complex numbers, consisting of numbers of the form where are real numbers, and...
But, as is common in this field, I don’t make public the observations that I made, and the next person who looks at the same problem would likely have to go through the same process of trial and error to work out what the main obstructions that are present are. So, as an ...
Similar optimization applies to other immutable objects like empty tuples as well. Since lists are mutable, that's why [] is [] will return False and () is () will return True. This explains our second snippet. Let's move on to the third one,...
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If is negative, then it has no ordered -partitions, because ordered -partitions of are tuples of positive integers that sum to , but the sum of a tuple of positive integers is always non-negative. If , then has no ordered -partitions, because ordered -partitions of are tuples of positiv...
Similar optimization applies to other immutable objects like empty tuples as well. Since lists are mutable, that's why [] is [] will return False and () is () will return True. This explains our second snippet. Let's move on to the third one,...
ObsessiveMathsFreak 406 8 Thread Necromancy! I'd like to bump this old thread to reopen discussion on the idea of covariance and contravariance. To begin on the wrong foot, I think that covariance and contravariance are in fact red herrings in the study of tensors, but ...
In the case of the second moment method, this allows us to compute correlations such as for “most” . The entropy method gives bounds that are significantly weaker quantitatively than the second moment method (and in particular, in its current incarnation at least it is only able to say ...
If there are no other hypotheses under consideration, then the two posterior probabilities , must add up to one, and so can be recovered from the posterior odds by the formulae This gives a straightforward way to update one’s prior probabilities, and I thought I would present it in the...
Similar optimization applies to other immutable objects like empty tuples as well. Since lists are mutable, that's why [] is [] will return False and () is () will return True. This explains our second snippet. Let's move on to the third one,...