Given v. when given v. an improper algebraic fraction when given

hhtt

Senior Member
Turkish
Original: Given an improper algebraic fraction, we must first use the methods of page 7 to obtain an expression which does not contain any improper fractions.

The original seems odd to me. For a proper usage, should it write "when given" or "an improper algebraic fraction when given ..."

Source:
Understanding Pure Mathematics by Sadler/Thorning

Thank you.
 
  • entangledbank

    Senior Member
    English - South-East England
    'Given' is in effect a preposition here. It started out as an ordinary use of the past participle, understood as 'when given' or 'if we are given', but it is now a set expression by itself.
     

    hhtt

    Senior Member
    Turkish
    'Given' is in effect a preposition here. It started out as an ordinary use of the past participle, understood as 'when given' or 'if we are given', but it is now a set expression by itself.
    What do you mean by "It started out as an ordinary use of ..." and "a set expression by itself"

    Thank you.
     

    entangledbank

    Senior Member
    English - South-East England
    Well, that's how we say it: that's what I mean by a set expression. We treat it like a preposition, as if it's similar to 'with an improper fraction'. We don't think of a person (a reader, a speaker) who is given something: no-one is giving anything to anyone. Contrast: 'I'll give you a number and you tell me its square root,' where someone is still giving (in the weak sense 'telling'). But originally people would have thought that way: if we are given an improper fraction, then . . .
     
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