I know the limit superior isn't always defined on function in general, but intuitively, I don't see how it could be undefined on a function with a finite range. However, I didn't find any sources discussing this.
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I know I could just edit your question, but it's important to tell you this: it's not limit superior, it's limes superior. – 5xum Jul 01 '15 at 09:12
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@5xum Are you sure about that? When I google it, I get "limit superior" for the English pages. I think "limes superior" is German. – Kelmikra Jul 01 '15 at 13:14
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Wow, you're right. I had no idea the entire english speaking word is using the wrong expression. And yes, I feel it is wrong. Because $\limsup$ us the "largest wall", and limes is wall in latin... – 5xum Jul 01 '15 at 13:16