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I was wondering what the difference between einfach and nur is.

einfach = just, simply
nur = just, simply, only

What other differences in usage are there?

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    I've edited your question a bit—personal details are of little importance to your question. Regarding the other (unrelated) questions: try to ask one per post, that makes them more useful, as they are easier to find for others. – user6191 Feb 10 '15 at 16:36
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I would say most common the following relation holds:

einfach = simple

nur = just, only

Examples (einfach meaning simple):

Es ist ganz einfach. = It's quite simple.

Es gibt eine einfache Erklärung. = There is a simple explanation.

Das ist einfach nicht wahr. = This is simply/just not true.

Examples (nur meaning just):

Wir müssen nur wollen. = We just have to want.

Beruhige dich, es ist nur eine Spinne. = Calm down, it is just a spider.

Examples (nur meaning only):

Wenn ich nur könnte! = If only I could!

Ich akzeptiere nur ein Ja! = I only accept a yes!

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    Indeed simple literally means (or is derived from a Latin word meaning) "onefold", which again literally translated to "einfach". – Carsten S Feb 10 '15 at 18:24
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    As I'm sure you know "simply connected" = "einfach zusammenhängend". I have always wondered if that is a slight mistranslation from the German, or if the English "simple" still retains enough the "onefold" connotation. – Carsten S Feb 10 '15 at 18:26
  • Yes, one says that a topological space is simply connected if you can connect any two points of that space by a path and you can continuously transform within that topological space any path connecting 2 points into any other path connecting the same 2 points. In case the space is not simply connected one can further examine the degree of connection by the fundamental group. Since onefold is in a way the simplest case the translation is quite ok? – user9256 Feb 10 '15 at 18:44
  • I meant that this is the same as $1$-connected in the sense of all homotopy groups up to the first vanishing. I am not sure if then number one is felt as much in "simply" as in "einfach". But maybe I am mistaken about the origin of the term "simply connected". – Carsten S Feb 10 '15 at 22:28
  • you are not mistaken. einfach zusammenhaengend falls in line with zweifach zusammenhaengend and n-fach zusammenhaengend. i assume that the unsystematic translation stems from the fact that einfach zusammenhaengend is used much much more often than the higher ones, so that beginners in the field might not even be aware of them. – peter Feb 11 '15 at 11:42
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Einfach means 'simple' or 'simply', and nur means 'only' or 'merely'.

Also, einfach can be used as an adjective or adverb, whereas nur is only an adverb (or conjunction), never an adjective.

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While I agree on the previous answers I would like to add that in some contexts both terms can be used – and can be even used together. This is mostly the case when you'd want to underline how simple and/or easy something is:

Du musst nur… (You just have to…)

Du musst einfach… (You simply have to…)

Du musst einfach nur… (You simply just have to…)

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