Sin(x) is a real number, not a degree; this is in radian measure. And it's true only near zero. The three symbols you cite are used in a looser sense....
What about: \sin (x)\approx x,\text{ }\sin (x)\cong x\text{ }for\text{ }x\approx 0 or the more mysterious \operatorname{s}(n)\sim t(n)\text{ for large...
Once one moves beyond 3D, higher dimensional "space" for me becomes an algebraic geometric concept rather than a reality. Very useful for predictions ...
As an ex-gymnast and climber, what you speak of is allowing the body to do what it does with no interference from other aspects of the mind. No thinki...
The best among us is but human, although I would agree that Tom Brady is a God. To equate the far end of a normal curve to a celestial being is beyond...
Geothermal energy does seem to have tremendous potential. There are about 100K people employed in the industry now according to Wiki. It's estimated t...
2x=3-4x Conditional equation, true only for select values of x {{\left( x+1 \right)}^{2}}\equiv {{x}^{2}}+2x+1 Identity, true for all or nearly all va...
O0ps, sorry, I meant the icon is a product in the complex plane of a BASIC program I wrote . In this instance, the program created the unexpected demo...
Certainly doctorates in physics or math - especially theoretical physics - can place one in the borderlands of philosophy and science. That was my poi...
N=1/N was a trick question. Sorry :cool: I now use Liberty Basic. I used Virtual basic until one morning I opened my computer and discovered that Micr...
Since we are talking about time, glancing over some of the papers in the metaphysics of time (the truly philosophical area) much concerns the A-theory...
Yes, that's true. But you don't have to read it all. It's good that one can write at length without a referee stepping in and limiting your flow. But ...
Good point. Fortunately that's not an issue normally in a mathematical discussion. Of course there may be other "rules" generating that finite sequenc...
Prove it continues. Mathematical induction is one way. Providing an algorithm is another. For example, I am working on a theorem now that has the prod...
Certainly n=1/n has solutions n=1 and n=-1. The other meaning I have in mind is quite different. Hint: I have written hundreds of mathematical program...
Clearly references suffice for existing knowledge. I'm speaking of steps in proofs that can be sketched out, knowing that experienced readers can fill...
Perhaps they do and we are incapable of understanding them. All of life are approximations. A right triangle is a Platonic ideal, but its approximatio...
This thread illuminates what it is to be a philosopher in modern times when all the sciences have progressed to the point that philosophical inquiries...
In Banno's example of color change, that change is of a dy/dx type. But as the eye moves from left to right, that change is of the dy/dt type. When x=...
Thanks for chiming in. I was a meteorologist for the USAF many years ago so its good to hear another give their opinions on TPF. I'd guess, yes. But C...
A function defined in set theory as a certain kind of collection of ordered pairs - not necessarily real or complex numbers - might be connected to th...
"Chaos theory" refers to certain dynamical systems having weaknesses allowing for minute changes to produce significant results through sequences of i...
Not necessarily. Millions of butterflies wiggle their wings in the Orient with no effect in San Francisco at all. Not all weather models are subject t...
I had a friend my age in the Air Force who had a BS in math, and he was an intelligence officer who planned to go to law school after his tour. He did...
Universities are increasingly using adjunct faculty, which is a travesty since the pay is extremely low and no benefits. Of course, if you are brillia...
Hello Z. I retired as professor of mathematics at a branch of a state university over twenty years ago, so its possible the undergraduate curriculum h...
Francisco Varela's homepage: F. Varela's Homepage A bit confusing for me. The math is pretty vague with the first appearance making no sense. A little...
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