Changes

Directory:Jon Awbrey/Papers/Differential Logic : Introduction (view source)

Revision as of 18:12, 19 June 2009

31 bytes added , 18:12, 19 June 2009

Line 28: Line 28:

|}

−

Back to the proposition <math>pq.\!</math> Imagine yourself standing in a fixed cell of the corresponding venn diagram, say, the cell where the proposition <math>pq\!</math> is true, as shown ~~here~~:

+

Back to the proposition <math>pq.\!</math> Imagine yourself standing in a fixed cell of the corresponding venn diagram, say, the cell where the proposition <math>pq\!</math> is true, as shown in the following venn diagram:

{| align="center" cellpadding="10"

Line 34: Line 34:

|}

−

Now ask yourself: What is the value of the proposition <math>pq\!</math> at a distance <math>\operatorname{d}p</math> and <math>\operatorname{d}q</math> from the cell <math>pq\!</math> where you are standing?

+

Now ask yourself: What is the value of the proposition <math>pq\!</math> at a distance of <math>\operatorname{d}p</math> and <math>\operatorname{d}q</math> from the cell <math>pq\!</math> where you are standing?

Don't think about it — just compute:

Line 49: Line 49:

Next question: What is the difference between the value of the

−

proposition <math>pq\!</math> over there, at a distance <math>\operatorname{d}p</math> and <math>\operatorname{d}q,</math> and the value of the proposition <math>pq\!</math> where you are satnding, all expressed in the form of a general formula, of course? Here is the appropriate formulation:

+

proposition <math>pq\!</math> over there, at a distance of <math>\operatorname{d}p</math> and <math>\operatorname{d}q,</math> and the value of the proposition <math>pq\!</math> where you are satnding, all expressed in the form of a general formula, of course? Here is the appropriate formulation:

{| align="center" cellpadding="6" width="90%"

Jon Awbrey

12,080

edits