Upper bounds are often considerably more difficult to establish : one either has to check all possible colourings to confirm the absence of a counterexample, or to present a mathematical argument for its absence.
22.
Instead, Crabtree argues that he is synthesizing already existing data and making a purely mathematical argument that estimates the probability of the number of new mutations that could result in cognitive deficits in future generations.
23.
Certain questions about Rosen's mathematical arguments were raised in a paper authored by Christopher Landauer and Kirstie L . Bellman which claimed that some of the mathematical formulations used by Rosen are problematic from a logical viewpoint.
24.
I mean I guess I'm asking for kind of like a mathematical argument as to why the convergence wouldn't contain more information . . . Thanks . talk ) 02 : 51, 31 January 2013 ( UTC)
25.
While Ms . Tyson has long devoted her attention to the hottest economic issues of the day, Stiglitz is a theoretician best known for his original ideas and mathematical arguments on issues of interest mostly to other economists.
26.
There is not really a clear distinction between computer calculations and proofs, as several of the proofs above, such as the 4-color theorem and the Kepler conjecture, use long computer calculations as well as many pages of mathematical argument.
27.
The appearance of the physico-mathematical argument in the " Reformed Astronomy " was the occasion for Stefano degli Angeli ( 1623 1697 ) to launch an " unexpected, somewhat disrespectful and sometimes flippant attack " on Riccioli and the argument.
28.
Chichilnisky says that she presented a mathematical argument for " necessary and sufficient conditions on the nonemptiness of the core " _ the core being the states of an economy upon which no group of agents can " improve ."
29.
In this interim, Jenkin provided a mathematical argument, the swamping argument, that showed that under the blending inheritance model any advantageous mutations which might arise in a species would be quickly diluted out of any species after just a few generations.
30.
On page 150 of " No Free Lunch " he claims he can demonstrate his thesis mathematically : " " In this section I will present an in-principle mathematical argument for why natural causes are incapable of generating complex specified information . ""
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