How to say a function that is differentiable everywhere is continuous. in Japanese

1)あらゆるあらゆる(arayuru) (adj-pn) all/every点(ten) (n) dot/point/mark/gidayuu musiciansで(de) (prt) indicates location of action/at/in/indicates time of action/indicates means of action/cause of effect/by/and then/so/indicates continuing action/ indicates certainty, emphasis, etc.微分可能no dictionary result, likely a conjigated verbno dictionary result, likely a conjigated verbな(na) (prt) connects adj to noun/indicates emotion or emphasis/command/prohibition関数関数(kansuu) (n) functionは(ha) (int) indicating a subject/yes/indeed/well/ha!/what?/huh?/sigh連続関数連続関数(renzokukansuu) (n) continuous functionですです(desu) (aux) be/is/are。(。) Japanese period "."    
arayuru ten de bibunkanou na kansuu ha renzokukansuu desu 。
Grammer form丁寧語 (Polite form)Polite form (teineigo)
convays a sense of politeness, used when speaking to strangers, people older than you, higher social status ect.
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Translation by thyc244
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