Does the word "contradictorily" exist?
I´ve been looking this word up in the dictionary and I can´t find it, but the thing is that if I use Google translate, it is the only place where it is translated. Does it exist or did I make it up?

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According to Oxford Dictionary, it is the adverbial form of "contradictory". :)

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But don't worry. If you wrote this as part of an essay, you probably won't have lost any marks. In spite of the two language errors, it's still clear what you mean.

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Ok, thanks again. You´re answers are always so accurate that I learn a lot from them.

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No, 'contradictorily' is wrong there. " [adverb] to what is thought" is grammatically incorrect - you need an adjective. You've also slipped in an extra 'it' which shouldn't be there - "what is thought" is a passive construction and the subject is 'what'.

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You´re absolutely right, but I´d like to know whether the sentence I wrote before would be right or not since I wrote it in an exam.

Evden çıkmadan dil öğrenme fırsatını kaçırmayın. Deneyimli dil eğitmenlerimizden oluşan seçkimize göz atın ve ilk dersinize şimdi kaydolun!