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Add Japanese language to my keyboard [duplicate]

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0 This question already has an answer here: 16.04 Japanese Text Input not working 1 answer 17.10 add Japanese input 1 answer I need help to install Japanese language in my PC. How can I add Japanese language to my Ubuntu? language japanese share | improve this question edited Jan 3 at 17:09 karel 58.1k 12 128 146 asked Jan 3 at 17:07

Is Lipschitz condition on derivatives essentially the same thing as epsilon-delta proof?

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1 $begingroup$ I am very confused about Lipchitz gradient/derivative. It's often used in machine learning proofs about gradient descent. Are Lipschitz and epsilon delta proof essentially the same thing? Lipchitz : A function $f:Drightarrow mathbb{R}$ is said to be a Lipschitz function, provided if there is a $L>0$ such that, $$|f(x) - f(y)| le L|x-y| text{ for all } x,y in D$$ Epsilon delta proof : For all $epsilon>0$ , there exists a $delta>0$ such that $$f(x)-f(y) < epsilon text{ if } |x-y| < delta$$ The two ideas are saying the same thing: if $f(x)$ and $f(y)$ differ by this much, then $x$ and $y$ differ by that much. Am I right? A related question posted here. derivatives epsilon-delta lipschitz-functions gradient-descent