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NuMachine, as powerful as Turing machine, but more intuitive in its working is described. Adding three more derivation rules...
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NuMachine, as powerful as Turing machine, but more intuitive in its working is described. Adding three more derivation rules to Elementary Arithmetic of Godel and calling it Sentient Arithmetic (SA), the incompleteness theorems are proved within SA, without using any metalanguage. Intuitive Set Theory (IST), a theory in which we do not have to deal with cardinals higher than aleph-null, is described. In IST, there is no Skolem Paradox and there are no nonLebesgue measurable sets.
Material Type:
Tutorial
Author:
Kannan Nambiar
Date Added:
Jun 13, 2001
Date Modified:
May 23, 2008
Peer Review for material titled "Foundations of Computer Science"
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Intellectual space is defined as the set of all proofs of mathematical logic, contained in The Book of Erdos. Physical and...
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Intellectual space is defined as the set of all proofs of mathematical logic, contained in The Book of Erdos. Physical and intellectual spaces are visualized making use of concepts from Intuitive Set Theory.
Material Type:
Reference Material
Author:
Kannan Nambiar
Date Added:
Jun 26, 2001
Date Modified:
May 21, 2008
Peer Review for material titled "White Hole, Black Whole, and The Book"
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An author's Snapshot for Foundations of Computer Science for the material found in MERLOT at...
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An author's Snapshot for Foundations of Computer Science for the material found in MERLOT at http://www.merlot.org/merlot/viewMaterial.htm?id=89637. This snapshot shows an overview of the material. This was created in the MERLOT Content Builder.
Material Type:
ePortfolio
Author:
Kannan Nambiar
Date Added:
Aug 11, 2011
Date Modified:
Aug 11, 2011
Peer Review for material titled "Foundations of Computer Science: A Snapshot"
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Godel has proved that there are formulas in Elementary Arithmetic, which will introduce contradictions, irrespective of...
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Godel has proved that there are formulas in Elementary Arithmetic, which will introduce contradictions, irrespective of whether we assume the formula itself or its negation. His proof is in metalanguage. Sentient Arithmetic (SA) adds three more derivation rules to EA and shows that the proof for incompleteness of SA can be given in SA itself without using any metalanguage.
Material Type:
Reference Material
Author:
Kannan Nambiar
Date Added:
Jun 25, 2001
Date Modified:
Apr 14, 2010
Peer Review for material titled "Sentient Arithmetic and Godel's Theorems"
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A complete analysis of Shannon's telegraph channel is given, making use of matrices with elements from a division ring. A...
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A complete analysis of Shannon's telegraph channel is given, making use of matrices with elements from a division ring. A notation is developed for representing the set of signals of a communication channel.
Material Type:
Simulation
Author:
Kannan Nambiar
Date Added:
Nov 07, 2001
Date Modified:
Dec 20, 2005
Peer Review for material titled "Shannon's Communication Channels and Word Spaces"
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The most popular format for publishing mathematics on the Web is the PDF, and HyperLaTeX is the program which allows us to...
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The most popular format for publishing mathematics on the Web is the PDF, and HyperLaTeX is the program which allows us to introduce hyper references in the PDF documents. This paper is a tutorial on using HyperLaTeX to produce PDF files.
Material Type:
Tutorial
Author:
Kannan Nambiar
Date Added:
Nov 30, 2001
Date Modified:
Dec 20, 2005
Peer Review for material titled "The Ecstasy of HyperLaTeX"
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It is not unusual that instructors get bogged down in the complex details of set theory, while teaching the foundations of...
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It is not unusual that instructors get bogged down in the complex details of set theory, while teaching the foundations of computer science. This paper is an attempt to help them from the quagmire.
Material Type:
Reference Material
Author:
Kannan Nambiar
Date Added:
Jan 22, 2002
Date Modified:
Dec 20, 2005
Peer Review for material titled "Two Open Problems and a Conjecture in Mathematical Logic"
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