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• Higher order votes
  Once again, we apply the Uniqueness Theorem to conclude that there is, essentially, just one such decision function. '''Theorem.''' A tally $f$ for comparisons that satisfies Stability and Triviality is
  41 KB (6,942 words) - 05:04, 22 June 2016
• Elections
  ...the non-emptiness of this set is a necessary condition for existence of an extension of $g$ from $M(K)$ to $K$. We will demonstrate later that this is also a su '''Theorem.''' A rating tally satisfies Independence if and only if there is such a ho
  33 KB (5,872 words) - 13:13, 17 August 2015
• Cochain complexes and cohomology
  '''Theorem.''' $$\dim C({\bf R}) = \infty.$$ '''Theorem:''' $H^0(K) = {\bf R}^m$, where $m$ is the number of path components of $|K
  17 KB (2,592 words) - 14:38, 14 April 2013
• Continuous vs discrete differential forms
  ...ative produces two discrete functions that don't satisfy the [[Fundamental Theorem of Calculus]].''</center> But the original function and its derivative do satisfy the theorem! The problem is created by the sampling itself. In fact, we can now describ
  9 KB (1,483 words) - 13:54, 13 April 2013
• Discrete functions
  The integral provides may be the answer. The ''Fundamental Theorem of Calculus'' states: Then the Fundamental Theorem of Calculus fails and, with it, one of ''the laws of physics''!
  15 KB (2,532 words) - 12:21, 11 July 2016
• Real analysis: final 2
  #State the extension of the Mean Value Theorem to functions $f:\mathbf{R}^{n}\rightarrow\mathbf{R}.$ ...prove the Contraction Principle. Give examples of functions for which the theorem does or does not apply.
  4 KB (582 words) - 20:29, 13 June 2011

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