In this case it tends to $+1$ and $-1$ which should mean that it does not have a cusp here and does not fall into one of the non differentiable categories. But it is not differentiable, so is this …

Apr 27, 2019 · In particular, the strongly monotonically increasing condition, for example, formalizes this idea of "don't look back." This definition enables some useful results we like - …

Wikipedia provides several different definitions of connectedness that they say are equivalent. For example, it says that a connected set is not the union of disjoint open sets. While this makes se...

Aug 18, 2018 · I’m currently learning it from scratch and I think that I pretty got the general idea: Supremum is largest limit of a set/sequence and infimum is the smallest. I’ve encountered the …

6 days ago · Definition of $C^ {1}$ on closure of open set Ask Question Asked 2 days ago Modified today

It is a theorem that immediately follows from the definition of congruence (depending on what definition you're using), From Wikipedia: "Two triangles are congruent if their corresponding …

Mar 24, 2023 · I want to define both real intervals and integer intervals, and I want to avoid duplication of effort. As such, I put together the following definitions. I wanted to share and get …

Since each equivalence class in this context represents all cars with a specific color and the quotient set contains all color groups (by definition), then the quotient set ultimately still …

Apr 27, 2018 · As with the definition of limit, the definition of continuity at a point can be formulated very nicely in terms of neighborhoods. This is done in the next result.

May 4, 2013 · 2 Another Wikipedia article of relevance is Characterizations of the exponential function. Which characterization is most appropriate to take to be the definition depends on the …