- #1
LawdyLawdy
- 3
- 0
Hello,
I am trying to teach myself set theory...main problem is, as an engineer, mathematical proofs were never exactly stressed in my curriculum. (Scary, right?)
The problem is stated as follows:
"Prove the following,
{x[itex]\in[/itex]Z|for an integer y, x=6y}={x[itex]\in[/itex]Z|for integers u and v, x=2u and x=3v}"
Z is the set of all integers.
(let's call the left side of the equation set A and the right side set B)
I can't seem to get my head around the "prose" of proofs.
I understand in order to prove a set A is equivalent to set B I need to show they have the exact same members ( A[itex]\subseteq[/itex]B and B[itex]\subseteq[/itex]A )
I also realize that if x=6y is in A then x=2(3y) and x=3(2y) is in B if you consider 3y and 2y the integers u and v, respectively.
I guess my question would be how to write it in an "acceptable" way and if the way I am going is the correct direction.(that is important too I suppose :p )
Apologies if this is a bit cluttered, this is my first time posting a math question on a forum and am working on getting the hang of it. Thanks in advance though for any help.
I am trying to teach myself set theory...main problem is, as an engineer, mathematical proofs were never exactly stressed in my curriculum. (Scary, right?)
The problem is stated as follows:
"Prove the following,
{x[itex]\in[/itex]Z|for an integer y, x=6y}={x[itex]\in[/itex]Z|for integers u and v, x=2u and x=3v}"
Z is the set of all integers.
(let's call the left side of the equation set A and the right side set B)
I can't seem to get my head around the "prose" of proofs.
I understand in order to prove a set A is equivalent to set B I need to show they have the exact same members ( A[itex]\subseteq[/itex]B and B[itex]\subseteq[/itex]A )
I also realize that if x=6y is in A then x=2(3y) and x=3(2y) is in B if you consider 3y and 2y the integers u and v, respectively.
I guess my question would be how to write it in an "acceptable" way and if the way I am going is the correct direction.(that is important too I suppose :p )
Apologies if this is a bit cluttered, this is my first time posting a math question on a forum and am working on getting the hang of it. Thanks in advance though for any help.