-
dlcs
In mathematics, a real number is a value that
represents a quantity along a continuous line. /ok good. ~ magnitudes. ~
continuous. to be sure: real incl all rational. as well as all
irrational. per prvs pgmrk Irrational Numbers [Incommensurability of
Magnitudes]: As a consequence of Georg Cantor's proof that the real
numbers are uncountable //countable is to be able to? count = ? list in
order, inclusively. comprehensively. ~ so is this the same fact as
incommensurability? th for those irrational lengths wh occur on the line
[and make up more of it than rational?] there is no unit?// and the
rationals (again, to be sure: a subset of former = real numbers)
countable /wh is not to say finite. rt?/, it follows that almost all
real numbers are irrational [*so, y: more irrational (in fact "almost
all") than rational. segments of a line. if finding possible divisions.
segmentatns. wld find more th cannot be descr by rational # than that
can. z1509 math
Irrational_number#Ancient_Greece - Wkp (redirected from Incommensurable magnitudes) /int -- and to #Ancient_Greece/
wikipedia.org
termed 'alogos', or inexpressible. /y:
irrational./ ...Bcs distinctn of number fr magnitude, geometry became
the only method cld take into account /well. not an account. logos.
better: only method cld display. deal with/ incommensurable ratios. so
Greek focus shifted away from numerical conceptions - algebra - to focus
almost on geometry /huh for that reason? as if numerical study fails/.
supposedly Hippasus made discovery out at sea, was thrown overboard by
his fellow Pythagoreans "for having produced /hmm/ an element in the
universe wh denied the doctrine that all phenomena in the universe can
be reduced to whole numbers & their ratios.”vs the assumption that
number & geometry inseparable. /but now again? w way of recognizing
irrational #s ? // irrational. like in Timaus, no incmmnsr in nous
making of world. but hv to go back incl stuff, receptacle. actualness
thereness. *in the universe* .. see 'Real Numbers' - most - all? -
irrational > nxt pgmrk. z1509 math essay a
-
textedit
en.wikipedia.org/wiki/Irrational_number
As a consequence of Cantor's proof that the real numbers are uncountable and the rationals countable, it follows that almost all [In mathematics, the phrase "almost all" has a number of specialised uses which extend its intuitive meaning] real numbers are irrational.[1]
l.[1] Cantor, Georg (1955) [1915]. Contributions to the Founding of the Theory of Transfinite Numbers. New York: Dover. //that is bk we read at sjc, rt? so I prob own? or was dffrnt Cantor re number.
Cantor's proof
Cantor's diagonal argument, also called the diagonalisation argument, the diagonal slash argument or the diagonal method, was published in 1891 by Georg Cantor as a proof that there are infinite sets which cannot be put into one-to-one correspondence with the infinite set of natural numbers. //wh are thus ~greater than? can compare amounts of one infite set to another?
(y I think so. was getting that. fr thinking re irrational numbers. more of than rational. in set of real.)
are uncountable
an uncountable set (or uncountably infinite set)[1] is an infinite set hat contains too many elements to be countable.
/mm. ok so y. can compare. like ~ infinite in more ways. a countably infinite set goes on forever. and perhaps as here in two directions, positive and negative rational numbers. infinite in extension.
*and infinitely divisible, right? can always divide in half. then express as ratio = rational. = any number can be expressed as ratio of integers. no? keep dividing in half takes into irrational ? (if infinitely divisible then how can count? right?
ALMOST ALL REAL NUMBERS ARE IRRATIONAL.
real numbers are uncountable.
rational numbers are countable.
_________
uncountable - countable = almost all // is that so? seems like wld be, but hv to articulate.
-
No comments:
Post a Comment