Hi, Is the following notation correct?(adsbygoogle = window.adsbygoogle || []).push({});

X = {x_{t}> max(x_{t-k},...,x_{t-1},x_{t+1},...,x_{t+k})|(t-k,...,t+k) ∈ T^{2k+1}∧ k ∈ ℕ\{0}} where T = [1,n]∩ℕ denotes the time periods over which x runs.

I basically want to say that X is the set of points that are local maxima in a neighbourhood of k points to the right and left of each point. my query is that, for instance, for k=3 and t=2, the condition would actually be :

x_{2}> max(x_{1},x_{3},x_{4},x_{5})

and (x_{1},x_{3},x_{4},x_{5}) is not a point in the space T^{7}

Maybe a better option would be to write t-k,...,t+k ∈ T instead of (t-k,...,t+k) ∈ T^{2k+1}...but it still seems unclear to me.

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# I Basic question about set theory

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