ε-δ function limit
Set
todo:
Rather define the set of all sequences which have a limit in the below sense
this is the domain of “lim” though of as function (on all sequences it would be a partial function)
| context | ⟨X,dX⟩ … metric space |
| context | ⟨Y,dY⟩ … metric space |
| context | f:X→Y |
| context | ξ∈X |
| definiendum | limx→ξ f(x)≡yξ |
| range | ε,δ∈R∗+ |
| postulate | ∀ε. ∃δ. ∀x. [ 0<dX(x,ξ)<δ ]⇒[ dY(f(x),yξ)<ε ] |
Discussion
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