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backprime

Denotes a backward-facing prime symbol, commonly used in mathematical notation to indicate specific variations or derivatives.

Overview

Serves as a specialized mathematical notation primarily found in advanced algebra and theoretical mathematics where backward-facing prime marks are needed to distinguish particular cases or transformations.

  • Often employed in abstract algebra to denote special cases or alternative versions of variables
  • Used in some mathematical texts to indicate specific types of operations or transformations
  • Provides a distinct alternative to the standard prime notation when multiple prime-like markers are needed
  • Particularly useful in contexts where both forward and backward prime notations need to be distinguished

Examples

Denoting the derivative of a function using the backprime notation.

f+g=(f+g)f^{\backprime} + g^{\backprime} = (f + g)^{\backprime}
f^{\backprime} + g^{\backprime} = (f + g)^{\backprime}

Using backprime to indicate the complement of a set in set theory.

AB=(AB)A^{\backprime} \cap B^{\backprime} = (A \cup B)^{\backprime}
A^{\backprime} \cap B^{\backprime} = (A \cup B)^{\backprime}

Multiple backprimes to denote higher-order derivatives.

f=d3fdx3f^{\backprime\backprime\backprime} = \frac{d^3f}{dx^3}
f^{\backprime\backprime\backprime} = \frac{d^3f}{dx^3}