Article 410 of misc.misc:
\nXref: puukko sci.math:453 misc.misc:410
\nPath: puukko!santra!tut!enea!mcvax!uunet!seismo!sundc!pitstop!sun!decwrl!decvax!ucbvax!jade!ig!uwmcsd1!csd4.milw.wisc.edu!markh
\nFrom: markh@csd4.milw.wisc.edu (Mark William Hopkins)
\nNewsgroups: sci.math,misc.misc
\nSubject: Re: Properties of Infinity
\nSummary: Laissez-Faire
\nKeywords: Infinity properties
\nMessage-ID:
\nDate: 17 Jan 88 02:49:51 GMT
\nReferences:
\nSender: daemon@uwmcsd1.UUCP
\nReply-To: markh@csd4.milw.wisc.edu (Mark William Hopkins)
\nOrganization: University of Wisconsin-Milwaukee
\nLines: 74<\/p>\n
In article ken@pdn.UUCP (Ken Auer) writes:
\n>For reasons which I’d rather not explain, I need to find out several
\n>properties of infinity and negative infinity which I’m sure are in some
\n>8th grade math book (which I don’t have immediate access to).
\n>
\n>I’ve got lots of educated guesses, but I really need concrete answers
\n>for things like the following (concrete meaning I can call a routine
\n>which can supply me with a concrete answer).
\n>
\n>\tinfinity is not even,
\n>\tinfinity is not odd,
\n>\tinfinity + infinity = infinity
\n>\tinfinity – infinity = ?
\n>\t.
\n>\t.
\n>\t.
\n>
\n>I really don’t want to start any highly theoretical discussions here, I
\n>just want to know what to do when some one tries to use infinity as s\/he
\n>would use a finite number in an equation, etc.
\n>
\n>————————————————————————–
\n>Ken Auer\t\t\t\t\tParadyne Corporation
\n>{gatech,rutgers,attmail}!codas!pdn!ken\t\tMail stop LF-207
\n>Phone: (813) 530-8307\t\t\t\tP.O. Box 2826
\n>\t\t\t\t\t\tLargo, FL 34649-9981
\n>
\n>”The views expressed above do not necessarily reflect the views of my
\n>employer, which by no means makes them incorrect.”<\/p>\n
Addition: Multiplication:<\/p>\n
Infinity + Finite = Infinity Infinity x Infinity = Infinity<\/p>\n
Infinity + Infinity = Infinity Infinity x Finite = Infinity,
\n but Infinity x 0 is undefined
\nInfinity + -Infinity can be
\nabsolutely anything finite or not Infinity x -Infinity = -Infinity<\/p>\n
-Infinity + Finite = -Infinity -Infinity x Finite = -Infinity,
\n with the same exception for 0 as before
\n-Infinity + -Infinity = -Infinity
\n -Infinity x -Infinity = Infinity
\nSubtraction:
\nSame as addition, with u-v treated as u+(-v):
\nwhere
\n-(Infinity) = -Infinity
\n-(-Infinity) = Infinity<\/p>\n
Division:
\nSame as multiplication, with u\/v treated as u x (1\/v):
\nwhere
\n1\/(-Infinity) = -0
\n1\/(Infinity) = +0
\n1\/(-0) = -Infinity
\n1\/(+0) = Infinity<\/p>\n
You’ll need to make the distinction between +0 and -0, if you’re going to say
\nanything useful about division with infinity.<\/p>\n
These rules are made in such a way that all the properties (+,x,-,\/) will
\nremain true when infinite limits are included. It is possible for a limit
\nto be infinite without its positive or negative sign being determined. This
\nlimit will represent the unsigned infinity. Its negative is itself and its
\nreciporical is 0 (without the + or – sign). You’ll need to use all three
\nkinds of infinity. Much of Calculus is devoted to resolving those limits
\ninvolving the undefined operations above, like<\/p>\n
Infinity – Infinity, Infinity x 0, Infinity\/Infinity<\/p>\n
There is a theory of infinitesimals based on what is known as Non-Standard
\nAnalysis. Its content is completely equivalent to Calculus. In fact, it is
\na reformulation of Calculus that matches very closely the original formulation
\nof Calculus as a calculation system for infinite and infinitesimal numbers.<\/p>\n
