The discussion revolves around proving the statement: If a|b and b|c, then a|c, within the context of integer divisibility in introductory analysis. Participants are exploring the implications of divisibility and the relationships between integers.
The discussion is active, with participants sharing their thoughts and attempts at the proof. Some guidance has been offered, particularly in terms of substitution and the importance of integer relationships. There is an acknowledgment of the challenges involved in transitioning from computational to proof-based mathematics.
Participants note the constraints of their homework assignments, including a limited number of problems and the expectation to submit all problems for grading. This has led to a sense of pressure in mastering proof techniques.
You have b in terms of a ? ...Windowmaker said:Homework Statement
Prove: If a|b and b|c then a|c.
Assume a, b and c are integers.
Homework Equations
none
The Attempt at a Solution
If a divides b then that means that there is a
real integer "r" that is ra=b .
and since we assume b divides c then c=bs.
After here I got stuck. I was thinking maybe substitute b and c for ar and bs, but it doesn't seem to get me anywhere. Thanks in advance.
If this is a concrete example, you'll need another number.Windowmaker said:Well I was thinking like we had 3|15. So a would be 3 and b would be 15. The r would be 5, so ra=b= 5*3=15. Or am I thinking about this wrong?
Well, I saw that you were almost there in your original post. I'd rather lead you to discover what's missing than to simply provide the bridge.Windowmaker said:Oh my goodness...First class on proofs its just simple substitution. Thanks man, cleared up a lot!