Is it true that every limit that takes on an indeterminate form can be evaluated?
Is it proper to say that a limit problem has a solution if the limit does not exist?
It does work. It is intended for dealing with change, and people do that successfully with it all the time. You are illustrating what I meant about discussing physics from the outside vs. the inside. I distinguished time in physics vs. time in everyday speech — a metatheory level distinction—...
I used to have difficulty with the concept of time dilation similar to what is expressed in the OP. The problem is that physics theory, or the way it is discussed or taught, is not explicit about definitions of terms. The key, as someone posted early on, is that "time is what a clock measures."...
I think that those two things — the meaning of time and the way in which it is measured — are always the same thing in the context of all branches of physics.
Yes. Too bad such precision isn't widely reflected in physics education, theory, and general discourse.
On another note, I suppose that it's just another one of those arbitrary and therefore unintuitive (to me) conceptual things about physics that what we've been discussing here is considered...
Ok, but won't there ALWAYS be some amount of energy dissipation? Not just theoretically, but an observed discrepancy between energy in and energy out? It seems sloppy and pointless to propose conservation of energy as an unqualified physical fact, rather than stating that energy in and energy...
That is utterly absurd; the role of computers in research scarcely extends beyond mere number-crunching. It takes a scientist to formulate hypotheses, design experiments, and interpret results.
What I don't understand is the role played by the symbol Δ. I understand modus ponens as
1. S
2. S → T
∴ T
That cannot be neatly applied to this proof:
1. Δ \vdash \forallvP would correspond to S
2. \vdash\forallvP → P(t/v) should correspond to S → T
However, the formula that corresponds to...
This is from a text on mathematical logic. The theorem to be proven (specialization):
If Δ \vdash \forallvP, then Δ \vdash P(t/v), provided that P admits t for v.
My confusion concerns the use of modens ponens in the proof:
Suppose that Δ \vdash \forallvP and P admits t for v. Then modus...
It's clear. You could possibly make it a bit more precise by specifying the universe of discourse, particularly since the sets A and B are made up of such disparate entities.
I know all of this. I didn't post the question because I thought that it is related to mathematical logic. "Logic" is in the name of the forum, so I assumed that discussion pertaining to all types of logic were permissible. If inductive logic is out of place in this forum, surely statistics is...
"Appraising Analogical Arguments"
I am self-studying an oldish text on introductory logic by Copi. The text lists some criteria by which arguments by analogy may be judged. Here are three of them:
"...the number of respects in which the things involved are said to be analogous."
"...the...
I had great difficulty learning from or even paying attention to lectures, so most of what I learned at university was from reading textbooks. I didn't interface with other students, and the primary benefit I got from professors was seeing how to solve problems by their examples. Laboratories...