| TRWBW | davidstrauss: how much experience do you have with saying non-sequitors? |
| davidstrauss | merus: he said "the def. that I have just says it's a relation where each input is related to one and only one output" that is defined as one-to-oneness well not quite |
| merus | That is not injectivity. |
| davidstrauss | TRWBW: cardinality theory has extensive coverage of functional mappings it's used as a tool for proving set cardinality |
| brick_ | this is a pretty basic set theory into class so i'm guessing this doesn't involve complex cardinality |
| davidstrauss | set theory and cardinality are complementary studies |
| TRWBW | brick_: davidstrauss said something irrelevant, now he's going off on a tangent because he's embarassed. you can ignore him. |
| brick_ | s/into/intro. anyways, a relation between X and Y is just the cartesian product of them? |
| TRWBW | brick_: yes |
| thief_grr | brick_: no |
| davidstrauss | a relation is a *subset* of the cartesion product |
| thief_grr | brick_: it's a subset of the cartesian product |
| TRWBW | davidstrauss: true |
| brick_ | So we'd have say {(a,u), (b,u), (c,u)}? |
| TRWBW | brick_: that's it. |
| thief_grr | brick_: this is a relation which happens to be a function brick_: while {(a, u)} is a relation which is not a function. unless you accept partial functions |
| lokie | hey guys |
| brick_ | maybe it's just the notation that's confusing me: If the question says "find all functions from X to Y" would writing the set {(a,u), (b,u), (c,u)} be appropriate? Mayhaps i'm just used to writing functions as f(x) |
| davidstrauss | yes, that is acceptable notation it's a finite relation, so the function it models has finite possibilities |
| lokie | if i had tripple integral e^z dV, and i'm converting it into cylinderical coordinates, and i got: 0 <= r <= sqrt(5); 0 <= z <= 1+r^2; 0 <= t <= 2PI; t is theta btw. i now have: tripple integral with the bounds i just listed, e^zr dr dt dz, can i split it up into e^z dz (r dr) ( dt) and intgrate them all seperately and multiply the answers at the end? |
| davidstrauss | thus, you can list them all |
| TRWBW | brick_: you could stick and extra {} around it to make it the set containing just that. |
| davidstrauss | TRWBW: even better |
| TRWBW | brick_: f(x)=u is probably acceptable too, but given the level of the question, i suspect you are doing basic function theory, and they might want you to write it explicitly in terms of the definition |
| Defty | % Solve[ 1/6*x + 3/2 == Sqrt[x], x] |
| mbot | Defty: {{x -> 9}} |
| Defty | % Solve[ D[1/6*x + 3/2,x] == D[Sqrt[x],x], x] |
| mbot | Defty: {{x -> 9}} |
| lokie | hm...why isn't that possible? I just attempted what I said above and i'm getting e^(1+r^2)-1 * 2PI * 5/2 |
| TRWBW | Defty: why don't you and mbot get a room? |
| Defty | i'm not sure how to ask her in private |
| lokie | o its a female? hott |
| TRWBW | Defty: you need to /identify yourself, then you can /msg mbot % 1+1 |
| Defty | muse ex machina.. |