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1
Philosophy of Mathematics: Selected Readings
If werestate the question inthe form:“Isit possible to establisha one toone
correspondence between theelements of a set of denumerably infinite ordinal
numbers ontheonehand, and aset of real numbersbetween 0 and1 on the
otherhand, both ...
Paul Benacerraf, Hilary Putnam, 1984
2
The World of Mathematics
set of all pairs of natural numbers is denumerably infinite. In order to understand
this we have merely to arrange the set of all pairs of natural numbers “diagonally”
as indicated in Figure 2, whereupon we at once obtain the one-to-one ...
3
Empiricism, Logic and Mathematics: Philosophical Papers
+ an_ix+an = 0 with integral coefficients a0, ax , • . . an, is denumerably infinite. At
this point, the reader may ask whether, in the last analysis, all infinite sets are not
denumerably infinite — that is, equivalent? If this were so, we should be sadly ...
Hans Hahn, B.F. McGuinness, 1980
4
L.E.J. Brouwer – Topologist, Intuitionist, Philosopher: How ...
In fact Cantor's diagonal method yields such a systematic method for the
continuum. Brouwer coined a new term for this phenomenon: We mean by a
denumerably unfinished set one, of which only a denumerable group can be
indicated in a ...
5
Handbook of Philosophical Logic
This implies that Cantor's diagonalization function Dm3(d,n,n) for the right matrix
m3 or special putatively conservative permutation of a supposedly complete
denumerably infinite list of rationals into the right matrix m2> can construct the ...
Dov M. Gabbay, Franz Guenthner, 2004
6
One Hundred Years of Intuitionism (1907-2007): The Cerisy ...
To be precise, he defined X as denumerably unfinished, if (1) only denumerable
subsets can be produced, and (2) there is for X a previously defined procedure
that for every such denumerable subset A automatically produced an element of
X ...
Mark van Atten, Pascal Boldini, Michel Bourdeau, 2008
7
Deducibility and Decidability
R. R. Rockingham Gill. those of the terms of σ: thus the concatenation of A.5 One,
and only one, formal language is considered in this book; its simple signs, called
letters, fall exhaustively and exclusively into classes as follows: —denumerably ...
R. R. Rockingham Gill, 2002
8
Applied Probability and Statistics
The number of elementary events in a sample space may be finite (S 1 and S2),
denumerably infinite (S3), or non-denumerably infinite (S4). Remark. A set is
called denumerably (or countably) infinite if we can establish a one-to-one ...
9
Mathematical Methods in Linguistics
Since A" is a denumerably infinite set, it has cardinality H0; its power set, i.e., the
set of all languages over A, has cardinality 2K° and is thus non- denumerably
infinite. Since the devices for characterizing languages which we will consider,
Ariz.
Barbara Partee, Alice ter Meulen, Robert Wall, 1990
10
Algebra: Based in Part on Lectures by E. Artin and E. ...
Finite sets and denumerably infinite sets are both called denumerable or
countable. Exercises 1.5. Prove that the number of elements in a union of two
mutually exclusive finite sets is equal to the sum of the numbers of the individual
sets.
B.L. van der Waerden, 2003
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How Can Mind Act On Matter?
That unfolding becoming of the biosphere, I claim cannot be finitely, or even denumerably infinitely, prestated, nor can it be mathematized. «NPR, Mar 10»
