On June 19, 2014, John Gabriel wrote: > On Thursday, June 19, 2014 8:51:03 PM UTC+2, Soap Research wrote: > > > On June 19, 2014, John Gabriel wrote: > > > > > > > > > > > > > > > > > > > > So what? It's valid. What does it matter which definition is used? > > > > > > > > > > > > > > > > > > > It changes EVERYTHING. > > > > It really changes NOTHING. A proof is valid no matter what definition is used. Does God love one definition more than another? > > > > > Using classical mathematics, your converse of MVT is false, having f(x) = x^3 as a counter-example. In your New Calculus, the converse of MVT is true, and f(x) = x^3 has no derivative. > > > > The converse is 'false' in mainstream mathematics only because of the misinterpretation of tangent line. > > > > > In classical mathematics, a tangent CAN cross f(x), while in your New Calculus, you introduced the concepts of half-tangent and finite tangent. > > > > That is false. Nowhere has the original definition of tangent line been changed. Don't believe what you read on the Wikipedia Moronica. There is not a shred of evidence that the definition was 'dismissed' as claimed, in any textbook. The original definition still stands. Thankfully Newton used the original definition, because guess what would have happened if he hadn't? > > > > You would never have known of NEWTON'S ROOT APPROXIMATION METHOD. > > > > Just stop and think about that very carefully! > > > > Here is some light reading for you: > > > > http://www.spacetimeandtheuniverse.com/math/4507-0-999-equal-one-563.html#post27336 > > > > > The tangent of f(x) = x in classical mathematics is the line itself, while it is non-sense in New Calculus. > > > > Seriously?! It's definition in the New Calculus is the same as that used by Newton. Works for me. In mainstream mathematics it has a dual nature: most times it is an actual tangent line, but then it implodes when an inflexion point is cosidered. > > > > > > > In classical mathematics, 0.999... = 1, not in your New Calculus. > > > > Very unfortunate mistake. I call it Euler's blunder. Goes back to bad, bad definitions. > > > > > Irrationals are legitimate in classical mathematics, but they are meaningless for you. > > > > Irrational numbers don't exist even in mainstream mathematics. Incommensurable magnitudes however, do exist. > > > > > Keep playing with your toys on your side. We'll play with ours. But don't expect to send a rocket to Mars or explain physical phenomena in a near future with your theories... > > > > Heh, heh. The NC will handle anything better than the flawed formulation you inherited from Newton and Leibniz. In fact, if earthlings ever get to the stars, they will be using the New Calculus. > > > > It's not a matter of if, but when the NC becomes mainstream mathematics. I may not be around, but it will happen in any event. The benefits in every way are so major that the NC cannot be dismissed or ignored any longer. :-)
You are really optimistic about the future of NC. I wouldn't be so confident if I were you.