maths~reader
New member
- Joined
- Oct 26, 2011
- Messages
- 8
Hi all,
I would like to clarify a question and my solution to it. Not quite sure if I’m on a right track. Please help me understand. If for example we assume scenario as follow
"Model a system to retain information of a cyclist results competed on a several events. The results are stored in the form of tuples containing Courses, Distance covered and the time taken"
\(\displaystyle [Course]\)
\(\displaystyle Distance == \mathbb{N}\)
\(\displaystyle Time == \mathbb{N}\)
\(\displaystyle Result == Course \times Distance \times Time\)
Details of course is basically tuple as follow
\(\displaystyle [Location]\)
\(\displaystyle Details == Location \times Distance \times Time\)
I now trying to a new global constant or axiomatic definition as it where for the following constraint
\(\displaystyle [Date]\)
\(\displaystyle results : Date \mapsto Result \)
\(\displaystyle details : Course \mapsto Details\)
Constraint
In at least one event the cyclist should have competed.
I came up with the following preposition. (In sorry not using the latex to put in axiom definition above. I tried to put in symbols but it dint work)
And also please note relation 'results' and details or partial function but not just \(\displaystyle \mapsto\). I couldn't find a command for partial functions symbol.
So this is my preposition for the above incomplete axiom
\(\displaystyle \forall\ y:dom(results) \bullet \exists\ r:ran(results) \bullet y \mapsto r \epsilon results\)
We assume that the cyclist competes just one event everyday. Would my above definition fulfils the constraint?
Please help in understand and thanks very much.
I would like to clarify a question and my solution to it. Not quite sure if I’m on a right track. Please help me understand. If for example we assume scenario as follow
"Model a system to retain information of a cyclist results competed on a several events. The results are stored in the form of tuples containing Courses, Distance covered and the time taken"
\(\displaystyle [Course]\)
\(\displaystyle Distance == \mathbb{N}\)
\(\displaystyle Time == \mathbb{N}\)
\(\displaystyle Result == Course \times Distance \times Time\)
Details of course is basically tuple as follow
\(\displaystyle [Location]\)
\(\displaystyle Details == Location \times Distance \times Time\)
I now trying to a new global constant or axiomatic definition as it where for the following constraint
\(\displaystyle [Date]\)
\(\displaystyle results : Date \mapsto Result \)
\(\displaystyle details : Course \mapsto Details\)
Constraint
In at least one event the cyclist should have competed.
I came up with the following preposition. (In sorry not using the latex to put in axiom definition above. I tried to put in symbols but it dint work)
And also please note relation 'results' and details or partial function but not just \(\displaystyle \mapsto\). I couldn't find a command for partial functions symbol.
So this is my preposition for the above incomplete axiom
\(\displaystyle \forall\ y:dom(results) \bullet \exists\ r:ran(results) \bullet y \mapsto r \epsilon results\)
We assume that the cyclist competes just one event everyday. Would my above definition fulfils the constraint?
Please help in understand and thanks very much.
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