Thanks for posting this, OP. I really enjoyed the video clip, and Prof. Mattuck's reply. You're right about it being not rigorously proved, but that is because it is intended as "motivation"--it motivates the definition of a continuous analogue to a discrete definition. My idea of a "rigorous...
Thanks for the reply!
What is bothering me is that Spivak doesn't give us a way to add the same number to both sides of an equality. I came up with the following way to do this, but it requires an additional "pre-postulate", that I call (P -1): If a is a number, then a = a.
Then:
If a...
Homework Statement
Not a specific exercise per se; just a question from reading the text. In working the proof shown at the bottom of page 4 (2nd edition), I realized that the step "If a + x = a,
then (-a) + (a + x) = (-a) + a" could not be justified by any of Postulates 1, 2, or 3. At...
You'll get better answers, I'm sure, but what I recall reading is that planets that orbit in planes at large angles to one another create gravitational perturbations that cause instability in one or more planets' orbits. The instability is evinced by planets changing their orbits to either...