Changes

<math>a_{i}=1</math> when <math>a_{ii}\neq1</math> and <math>a_{i}=2</math> when <math>a_{ii}=1</math>.

<math>a_{i}=1</math> when <math>a_{ii}\neq1</math> and <math>a_{i}=2</math> when <math>a_{ii}=1</math>.

Therefore <math>a</math> is not in the list, so we have a contradiction and our assumption is false, the numbers in <math>[0,1]</math> are not countable. Therefore <math>\mathbb{R}</math> is uncountable.<ref>A. N. Kolmogorov, ''Introductory Real Analysis''. ISBN 978-0486612263.</ref>

Therefore, <math>a</math> is not in the list, so we have a contradiction and our assumption is false, the numbers in <math>[0,1]</math> are not countable. Therefore, <math>\mathbb{R}</math> is uncountable.<ref>A. N. Kolmogorov, ''Introductory Real Analysis''. ISBN 978-0486612263.</ref>

==Diagonalization and the Existence of God==

==Diagonalization and the Existence of God==

Some have cited diagonalization as a formal challenge to [[Saint Anselm]]'s [[ontological argument]] for the existence of God. In summary, Anselm argued that there must be a greatest idea and what could be greater than God? Therefore God exists.<ref>http://www.ephilosopher.com/e107_plugins/forum/forum_viewtopic.php?104130</ref>

Some have cited diagonalization as a formal challenge to [[Saint Anselm]]'s [[ontological argument]] for the existence of God. In summary, Anselm argued that there must be a greatest idea and what could be greater than God? Therefore, God exists.<ref>http://www.ephilosopher.com/e107_plugins/forum/forum_viewtopic.php?104130</ref>

However, diagonalization argues that no greatest idea can exist: quite bluntly, God is infinite, therefore He can be diagonalized to produce an even greater infinite.<ref>''Topo-philosophies: Plato's Diagonals, Hegel's Spirals, and Irigaray's Multifolds'', Arkady Plotnitsky. In ''After Poststructuralism: Writing the Intellectual History of Theory'' Tilottama Rajan, Michael James.</ref>

However, diagonalization argues that no greatest idea can exist: quite bluntly, God is infinite, therefore He can be diagonalized to produce an even greater infinite.<ref>''Topo-philosophies: Plato's Diagonals, Hegel's Spirals, and Irigaray's Multifolds'', Arkady Plotnitsky. In ''After Poststructuralism: Writing the Intellectual History of Theory'' Tilottama Rajan, Michael James.</ref>