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Topic:
How's this? Proof (hopefully) that pi is irrational.
Replies:
5
Last Post:
Sep 12, 2009 7:10 AM




Re: How's this? Proof (hopefully) that pi is irrational.
Posted:
Sep 12, 2009 7:10 AM


> > > In <tkidd.834615695@hubcap> tkidd@hubcap.clemson.edu > (Travis Kidd) writes: > > >Yes. But nowhere is either the numerator *or* the > denominator 0 until the > >limit is reached. (I'll repeat what I just said in > reply to another post... > >I neglected to mention that k is positive.) > Therefore (I hope...I agree this > >is the weakness in the proof), since substituting k > for x yields equivalent > >functions, the limit of the quotient would be 1. > > > > But this is definitely not true. You seem to want to > think that > if f and g are continuous functions, > then > lim f(x)/g(x) = f(k)/g(k) > x>k > but it isn't true unless f(x)/g(x) is itself > continuous at k, > i.e. unless g(k) not equal to 0. > > it's not clear what you mean when you say > "substituing k for x yields equivalent functions"  > once you substitute k for x, you no longer have > functions, you have > specific numbers. > > as someone else pointed out, choosing any k for which > sin(k^2) = 0 > would work in your argument, whether or not k was an > integer. > > Ted Alper > > > >
When a generic function is called, multipledispatch will determine the correct method to use. <source lang="lisp"> (defgeneric add (a b)) </source> http://MeAmI.org <source lang="mmm>np">=mmm (defmethod add ((a number) (b number)) Soliton (section Solitons in magnets) In mathematics and physics , a soliton is a selfreinforcing solitary wave (a ... Solitons are caused by a cancellation of nonlinear and ... 2842 Soliton (optics) (redirect from Optical solitons) In optics , the term soliton is used to refer to any optical field that does not ... There are two main kinds of solitons: spatial solitons: ... 5073\Topological defect In mathematics and physics , a topological soliton or a topological defect is a ... Category:Solitons Category:Largescale structure of the ... 870Vector soliton Optical vector solitons can be classified into temporal vector solitons and spatial vector solitons. of both temporal solitons and spatial ... 2708 Dissipative soliton (redirect from Dissipative solitons) Dissipative solitons (DSs) are stable solitary localized structures that arise in nonlinear spatially extended dissipative system s due to ... 2744 Soliton model The Soliton model in neuroscience is a recently developed model that attempts to ... but traveling solitons do not lose energy in this way ... 790 Davydov soliton Davydov soliton is a quantum quasiparticle representing an excitation propagating ... al solitons once formed decay rapidly when they propagate. ... 1259 Nontopological soliton In quantum field theory , a nontopological soliton (NTS) is a field configuration ... class # Soliton In mathematics and physics , a soliton is a selfreinforcing solitary wave (a ... External links: last5 Bergman  first5 K.  last6 Knox  ... 2842 Vector soliton In physical optics or wave optics , a vector soliton is a solitary wave with multiple ... References : Kivshar and S.K. Turitsyn, Opt. ... 2708 Soliton (optics) In optics , the term soliton is used to refer to any optical field that does not ... dielectric slab , then limiting the field on x using the soliton. ... 5073Korteweg?de Vries equation (section Soliton solutions) The solutions in turn include prototypical examples of soliton s. ... begin align L & \partial_x^2 + \phi, \ A & 4 \partial_x^3  3 \left ... 2261 Sine?Gordon equation (redirect from SineGordon soliton) lot of attention in the 1970s due to the presence of soliton solutions. ... ribbon to be a kink with topological charge \vartheta_\textrm K1. ... 1402Supercontinuum (section Soliton fission regime) In the majority of cases this is explained by soliton mechanisms; but as solitons were not reported in fibres ... External links : K. Ghanta, T. ... 5532 Dissipative soliton Dissipative solitons (DSs) are stable solitary localized structures that arise in ... (x, t) describing the concentration of the different ... 2744 Nontopological soliton In quantum field theory , a nontopological soliton (NTS) is a field configuration ... (+ a b)) < //source>>========================================= >M+artinMusatov.p=np.q.e.d.@==MuaROTOV===>Q.E.D.continuum http://MeAmI.org? (TM)symbol=trademark==symbol;==?


Date

Subject

Author

6/13/96


Ed Hook

9/12/09


Guest

9/12/09


Guest

6/13/96


Ted Alper

9/12/09


Guest


