helping group together items so that they become easier for programs/computers/machines/algorithms to process accurately and quickly. what does it mean to nest parentheses? nesting parentheses occurs when one set appears within another set – it’s sort of like putting one box inside another box ...
What does ^ mean in mathematics? Find the value(s) of omega for which y = cos omega t satisfies d 2 y /d t 2 + 36 y = 0 . What is an antisymmetric relation in discrete mathematics? How does the LHS get reduced to RHS? \frac{1}{\omega i} + \frac{e^{-2i \omega \tau{...
So what does distributive property mean in math? The distributive property describes how we can distribute multiplication over addition and subtraction.Distributive Property Formula (Bold)According to the distributive property, an expression of the form A(B+C) can be solved as...
What is model theory in math? What does the notation 2^\mathcal{S}, where \mathcal{S} is a set, denote? How does the LHS get reduced to RHS? \frac{1}{\omega i} + \frac{e^{-2i \omega \tau{\omega i} + \frac{1- e^{-2i \omega \tau{\omega^2 \tau} = \frac{2e^{...
In the case of Erdös-Renyi graphs, we don’t have mean zero and the Rudelson-Vershynin Littlewood-Offord theorem isn’t quite applicable, but by working carefully through the approach based on the Nguyen-Vu theorem we can almost recover (1), except for a loss of on the RHS. As ...
In terms of random matrices, this is asserting that the top minor of a random matrix has spectral measure approximately equal to that of an arithmetic mean of independent copies of , so that the process of taking top left minors is in some sense a continuous analogue of the process of ...
Plugging into (*)'s RHS, we get: Then we get 1 = 1, so (*) is true at n = 1.There; we've shown that (*) works in some particular, named place. But does it work anywhere else?Well, that was our problem in the first place: we already knew that (*) worked in a few ...
Since, LHS = RHS, we can say that our result is correct. In case we find that LHS ≠ RHS, this means that there is some error in our division and either the quotient or the remainder is incorrect and we need to revisit our solution. Long Division While it is quick and easy to div...
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Before we do the proof, which is quite short, it’s important to point out that the target dimensioncdoes not depend on the original dimension! It only depends on the number of points in the dataset, and logarithmically so. That makes this lemma seem like pure magic, that you can take...