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What does the letter epsilon signify in mathematics? The greek letter epsilon, written ϵ ϵ or ε ε, is just another variable, like x x, n n or T T Conventionally it's used to denote a small quantity, like an error, or perhaps a term which will be taken to zero in some limit It's possible that you are confusing it with the set membership symbol ∈ ∈, which is something different When you see x ∈ X x ∈ X it means that X X is a set
notation - Backwards epsilon - Mathematics Stack Exchange What does the $\\ni$ (backwards element of) symbol mean? It doesn't appear in the Wikipedia list of mathematical symbols, and a Google search for "backwards element of" or "backwards epsilon" turns
How exactly do I prove the limit of a sequence using the $\epsilon$-$N . . . I understand how to use the ϵ ϵ - N N method when proving the limit of a sequence However, I feel as though it is just a big guessing game Take this for instance; The sequence below converges to 5 as n tends to ∞ ∞ But, in proving this, there is a lot I still find confusing
Computing a limit using the $\\epsilon$-$\\delta$ definition. I would like to resolve a paradox I'm arriving at when I want to use the $\\epsilon$-$\\delta$ definition of limits to actually compute limits I learned a theorem in Apostol's Mathematical Analysis
real analysis - Calculus, how to find the value of delta in $\epsilon . . . I think your proof is equivalent, but it just doesn't follow the typical order of ϵ ϵ -δ δ -proof In ϵ ϵ -δ δ proof one discovers what δ δ one needs, by "looking in the future" in the proof So you do things starting from the "Suppose 0 <|x − 4| <δ 0 <| x − 4 | <δ " and then decide on the δ + 12δ + 48δ + 64 δ + 12 δ + 48 δ + 64 part, what δ δ you need in order to make