In the mathematical theory of Galois representations, a choice of algebraic closure of the rationals and an embedding of this algebraic closure in the complex numbers (e.g. section 5) is usually necessary to frame the background setting, but I never hear “the algebraic closure” or “the embedding,” instead “an algebraic closure” and “an embedding.” Thus I never forget that a choice has to be made and that this choice is not necessarily obvious. This is an example from mathematics where careful language is helpful in tracking background assumptions.
This is an example from mathematics where careful language is helpful in tracking background assumptions.
I wonder how the mathematicians speaking article-free languages deal with it, given that they lack a non-cumbersome linguistic construct to express this potential ambiguity.
In the mathematical theory of Galois representations, a choice of algebraic closure of the rationals and an embedding of this algebraic closure in the complex numbers (e.g. section 5) is usually necessary to frame the background setting, but I never hear “the algebraic closure” or “the embedding,” instead “an algebraic closure” and “an embedding.” Thus I never forget that a choice has to be made and that this choice is not necessarily obvious. This is an example from mathematics where careful language is helpful in tracking background assumptions.
I wonder how the mathematicians speaking article-free languages deal with it, given that they lack a non-cumbersome linguistic construct to express this potential ambiguity.
Thanks for sharing this.