- #1
Nano-Passion
- 1,291
- 0
I know from linear algebra that you can take two things, and if they are equal to each other then you can simply substitute different variables to develop a proof of a different statement.
For example take,
w = a
w = z + k
therefore proof would posit that a = z + k
But my dilemma lies in what my physics book sometimes does. It derives a "proof" by taking two equations and dividing them by each other to attain a different statement.
For example,
w = a
b = k
[tex]\frac{w}{b}=\frac{a}{k}[/tex]
? This baffles me. What mathematical theorem or algebraic statement let's us derive something by taking two equations and dividing them by each other? There doesn't seem to be any connection or logic between steps.
For example take,
w = a
w = z + k
therefore proof would posit that a = z + k
But my dilemma lies in what my physics book sometimes does. It derives a "proof" by taking two equations and dividing them by each other to attain a different statement.
For example,
w = a
b = k
[tex]\frac{w}{b}=\frac{a}{k}[/tex]
? This baffles me. What mathematical theorem or algebraic statement let's us derive something by taking two equations and dividing them by each other? There doesn't seem to be any connection or logic between steps.