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What's the difference between ved and kender?

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What's the difference between ved and kender? Both of which are the present tense forms of at vide and at kende meaning to know in English

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Here you can read, in depth, the distinctions between the words ved and kender so you can feel confident that you're using them correctly. 

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At vide 

Verb Conjugation: vid, at vide, ved, vidste, har/havde vidst

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Knowledge
The simple answer is that at vide or ved is your knowledge: to have sure information about something, to have enough experience to know something is sure or true.  
 
Knowledge, sure information, experience​
 
Det er vildt, hvor meget han ved om fodbold. 
It's crazy how much he knows about football.
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Det er rart at vide, at hun har det godt.
It's nice to know she's doing well.  
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To have an idea about what will happen or how someone will act​
 
Jeg vidste at hun ville spise min kage.  
I knew she'd eat my cake.
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Det er umuligt at vide, hvad hun laver.  
It's impossible to know what she's doing. 
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Have knowledge about the existence of something​
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Sortkaffe er det bedste jeg ved. 
Black coffee is the best thing I know.​
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En kold øl på en varm sommerdag. Det er bare det bedste jeg ved. 
A cold beer on a hot summer day. It's just the best thing I know.
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There are several other nuances and uses of the word vide, but these are arguably the most common
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Kender

Verb Conjugation: kend, at kende, kender, kendte, har/havde kendt

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So, whereas at vide refers greatly to the knowledge you have, at kende on the other hand refers mostly to what you are familiar with, that is, for example: places, people, books, movies, items, systems, etc.

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To be familiar with, to know a person​
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Hvor godt kender du København?
How well do you know Copenhagen? 
 
Kender du ikke min far?
Don't you know my dad? 
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Hun kender vejen. 
She knows the way.
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To know a system and thus how to use it
 
Alle kender alfabetets bogstaver. 
Everyone knows the letters of the alphabet.
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Jeg kender faktisk programmet rigtig godt. 
I actually know the program really well. 

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To perceive something as identical as previously seen, i.e. a person, a person's personality, building, a design etc (genkende = recognize)
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Hun sagde, at hun næsten ikke kunne kende dig.
She said that she almost couldn't recognize you.
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Kan du ikke kende bygningen?
Don't you recognize the building?
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To have/have had a sexual relationship
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Han har kendt mange kvinder.
He's known/been with many women.
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