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UID:/NewsandEvents/Archives/2015/newsitem/6870/8-M
 ay-2015-Cool-Logic-Ugur-Dogan-Humboldt-University-
 of-Berlin-
DTSTAMP:20150430T000000
SUMMARY:Cool Logic, Ugur Dogan (Humboldt Universit
 y of Berlin)
ATTENDEE;ROLE=Speaker:Ugur Dogan (Humboldt Univers
 ity of Berlin)
DTSTART;TZID=Europe/Amsterdam:20150508T173000
DTEND;TZID=Europe/Amsterdam:20150508T183000
LOCATION:ILLC Seminar Room (F1.15), Science Park 1
 07, Amsterdam
DESCRIPTION:In this talk, we will construct the se
 t of Hyperreal Numbers using the help of Model The
 ory. The set of Hyperreal Numbers is a field conta
 ining real numbers with the addition of "infinitel
 y small" and "infinitely big" numbers.  We will be
 gin with some historical background of Newton's (a
 nd Leibniz's, as well) work (differentiation) and 
 why he needed the concept of "infinitely small" nu
 mbers. Then to construct the set of Hyperreal Numb
 ers, we will introduce some Model Theoretic concep
 ts (such as languages, structures, sentences and e
 lementarily equivalence) and Los's Theorem. Then, 
 we will construct the nonstandard extension of the
  set of real numbers which we will call "the set o
 f Hyperreal Numbers" and we will proceed with exam
 ples of some actual hyperreal numbers and the exte
 nsions of some classical functions from standard a
 nalysis, such as exponential function and trigonom
 etric functions. If time permits, we will see some
  basic theorems in Nonstandard Analysis, such as R
 obinson's Compactness Criterion.  For more informa
 tion, see https://www.illc.uva.nl/coollogic/ or co
 ntact coollogic.uva at gmail.com
X-ALT-DESC;FMTTYPE=text/html:\n        <p>In this 
 talk, we will construct the set of Hyperreal Numbe
 rs using the help of Model Theory. The set of Hype
 rreal Numbers is a field containing real numbers w
 ith the addition of &quot;infinitely small&quot; a
 nd &quot;infinitely big&quot; numbers.</p>\n      
   <p>We will begin with some historical background
  of Newton's (and Leibniz's, as well) work (differ
 entiation) and why he needed the concept of &quot;
 infinitely small&quot; numbers. Then to construct 
 the set of Hyperreal Numbers, we will introduce so
 me Model Theoretic concepts (such as languages, st
 ructures, sentences and elementarily equivalence) 
 and Los's Theorem. Then, we will construct the non
 standard extension of the set of real numbers whic
 h we will call &quot;the set of Hyperreal Numbers&
 quot; and we will proceed with examples of some ac
 tual hyperreal numbers and the extensions of some 
 classical functions from standard analysis, such a
 s exponential function and trigonometric functions
 . If time permits, we will see some basic theorems
  in Nonstandard Analysis, such as Robinson's Compa
 ctness Criterion.</p>\n    \n        <p>For more i
 nformation, see <a target="_blank" href="https://w
 ww.illc.uva.nl/coollogic/">https://www.illc.uva.nl
 /coollogic/</a> or contact <a class="email">coollo
 gic.uva <span class="at">at</span> gmail.com</a></
 p>\n    
URL:/NewsandEvents/Archives/2015/newsitem/6870/8-M
 ay-2015-Cool-Logic-Ugur-Dogan-Humboldt-University-
 of-Berlin-
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