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There are many ways of interpreting "contradiction" in mathematics. Some meanings are:

  • Contradiction as in proof. You attempt to give the counter-proof of the theorem, but the counter-proof fails to work.
  • Contradiction as in mathematical logic. If biconditional fails, we include the slash through the double arrows pointing left and right at opposite directions.
  • Contradiction as in negation of the clause.
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Q: What is contradiction in algebra?
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