and several hours of my precious time to prove that 7 + 2 ≠ 10, or thereabouts.
Time and effort well spent methinks; I can now prove that any n + m ≠ k, when n + m ≠ k; ah! can I?
There may be interpretations where...you never got that sentances/theorems stuff did you neil... ?
Does 7 + 2 = 10? In some ring, space, domain or field?
No you are OK, if Q holds for an interpretation and you prove something using the sentances, then anything you prove holds for that interpretation.
But maybe not for an other interpretation where Q holds?
This is how maths fucks with your head; and why it is important to me to do it.
two and one-half pages
and several hours of my precious time to prove that 7 + 2 ≠ 10, or thereabouts.
Time and effort well spent methinks; I can now prove that any n + m ≠ k, when n + m ≠ k; ah! can I?
There may be interpretations where...you never got that sentances/theorems stuff did you neil... ?
Does 7 + 2 = 10? In some ring, space, domain or field?
No you are OK, if Q holds for an interpretation and you prove something using the sentances, then anything you prove holds for that interpretation.
But maybe not for an other interpretation where Q holds?
This is how maths fucks with your head; and why it is important to me to do it.