Terry Tao, UCLA Neo-Classical Methods in Discrete Analysis simons.berkeley.edu/talks/terr...
Пікірлер: 32
@MrYoumitube5 ай бұрын
I have no idea what Terry is talking about, I just enjoy watching the supremely smart and humble do their work.
@chandrapandey8226 жыл бұрын
That's a good and coincise talk, really good lecture. I really like how he provides good enthusiasm of the topic beforehand.
@hztm7776 жыл бұрын
Outstanding!
@kolomgorov2 жыл бұрын
Really wonderful!
@StephenPaulKing7 жыл бұрын
Are we limited to monotonic sequences?
@suyashsharma68302 жыл бұрын
Terence tao legend!!
@StephenPaulKing5 жыл бұрын
The analogue of Pontryagin duality for representations?
@StephenPaulKing7 жыл бұрын
I love the reference to approximate groups!!!
@StephenPaulKing7 жыл бұрын
Woah! I see shades of Aumann's agreement theorem in the x_n /elem X_n formal definition!
@davidwilkie95515 жыл бұрын
High quality Teaching such as presented by Professor Tao, makes the working of processes available to see for Students. From which the philosophical "Essence", the essential (amplitude and frequencies modulation) communication skills are interpreted and perceived. (Commentary) As yet another amateur (bridging) observation.., the frequent objective of math-phys-chem by philosophy is to unify Science in one word-concept, like "Universe", = one-turning, or Superspin connection etc, by following the vernacular of different fields and establishing from those path-aspects, a Correspondence in Principle. The reverse is true, (in principle of course), WYSIWYG in QM-TIMING substantiation, so the methodology of "proofing" in Mathematics that is all about improving techniques derived from empirical perceptions adapted to physical technology, eg after the Pure Mathematics, for Physics and Engineering, .. and can be observed to be self-defining, and so realised from the natural experiment of evolution, ..and then discovered by research. Therefore the common factor in Science is the "=" formulation, the "line of approach", observable identity, such as the axial-tangential visualisation of Polar-Cartesian Coordination in Perspective, ..of the coordinate zones "outside-inside" macro-micro formulae balanced at Zero. In which "outside" is the empty spacing of positioning excluded from rational/unitary modulated connection of e-Pi-i flat-space resonance, and "inside" is the Numerical superposition singularity of relative micro states/fractal of unity, but everything = one line of identification graphically/symbolically in the natural language of math-philosophy, ..quantized qualities of QM-Time. (= Almost incomprehensible simplicity of "All things Connected", taken for granted in developmental experience) Science and perceptions, Natural Philosophy, is Evolution and Life, (reiteration of identification imagery). "Discrete" is self-referencing connection, or reflection-imaging, single sided superposition, similar in concept to the characterization of "Majorana" a particular coordinate compound modular identity, in Continuity. Eternal continuous connection is the absolute Limit, or Potential Probability = 1, recognised in image-symbol components of reflection-resonance divisions/multiples, and balanced formulae.., = at Zero difference. The implication is that "zero or nothing" is the Real "inside-finite" limit-boundary of the unity-connection substantiation of existence in QM-TIMESPACE, in self-defining terms. Ie a real number exists in temporal quantum information terms as a fractional-fractal, dualistic algerbraic identity of unity and "image-inary" discrete dimensional numerical multiples. "Trivial" doesn't necessarily mean comprehensible(?).
@theemptyset7154 жыл бұрын
Why I think he was a student at the beginning?
@WriteRightMathNation6 жыл бұрын
Has anyone any idea who answered the question about ultraproducts by saying that he explained something to Tarski using them? I did not get it all, and I could not recognize his voice.
@sethstafford91506 жыл бұрын
I think the person who talked about using ultraproducts to prove the compactness theorem in 1958 was likely Dana Scott, who was a student of Tarski's for a while, then switched to Alonzo Church. en.wikipedia.org/wiki/Dana_Scott
@evmfacr Жыл бұрын
Did anybody get what he explained who Tarski?
@StephenPaulKing7 жыл бұрын
I am reminded of the Banach-Tarski paradox...
@deltaoperator7707 Жыл бұрын
Mr T of Math.
@BourneGoblinАй бұрын
AHmazing ❤
@CdosvirusexeАй бұрын
awesome
@klimentserafimov99246 жыл бұрын
Aren't the hypereals the same as Conway's surreal numbers?
@estring1234 жыл бұрын
no their not. ur an idiot. hyper reals here mean non standards reals. surreals are a proper class, far bigger than hyper reals. u r a moron.
@unbearableunspeakablepaina14453 жыл бұрын
@@estring123 No need to call him a moron, moron.
@soyokou.28106 ай бұрын
No
@TheRevAlokSingh4 ай бұрын
yes, under NBG. see philip erlich's work on 'absolute arithmetic continuum' @@soyokou.2810
@tweeweekes530910 жыл бұрын
So prof Tao. As part of an on going discussion I just wanted to clarify that with the non standard creation of reals we can say as you have noted that the limit of 1/n as n goes infinity does not equal 1 (unlike the standard construction of reals where it is zero and you note no one really uses the standard construction of reals anymore). This leads me to note that with this inifintesmal between limit before zero we can also then say that 0.999... does not equal one in the non standard construction of reals (which include hyperreals ie infinitesmals).
@tweeweekes530910 жыл бұрын
That is , the limit of 1/n as n goes to infinity does not equal ZERO (typo previously) in the non standard construction of reals. Also 0.999... does not equal 1 in the non standard construction of reals. Unlike the standrad construction of reals.
@EmperorZelos10 жыл бұрын
***** Where here?
@EmperorZelos10 жыл бұрын
***** He says it is important that the reals exists and not that you use that method of dealing with them as it is cumbersome. And he says that non-standard is an expansion of the reals meaning all truths in standard reals are equally true and valid in non-standard aka hyperreals. so 0,(9)=1 still,
@xiaoheidan7 жыл бұрын
W
@tgx35293 жыл бұрын
I think, that prof Tao suppose that 0 is not natural number, 1/n where n is natural number has the limit, this limit is not natural number. For same people is not 0 natural number. Here in Czech Republic is 0 in theory sets, in mathematic analysis, but not natural number only for students younger 18 years (before then they go to University). We have very much differences, in CZ exists derivative when is limit infinity, in USA doesn't ....
@estring1234 жыл бұрын
i think math is more concerned with using discrete/linear structures to analyze continuous structures. why does he give no opposite direction examples?
@TheRevAlokSingh4 ай бұрын
this entire talk is about how to do that. the 'continuous counterexample' around the 55m-1h mark is an example of that technique. graph theory is a field hugely influenced by manifold theory, because manifolds are continuous graphs, made precise by the nonstd POV