Authors
Topics
Lists
Pictures
Resources
More about Georg Cantor
Georg Cantor -
Variable
Quotes
5 Sourced Quotes
View all Georg Cantor Quotes
Source
Report...
As for the mathematical infinite, to the extent that it has found a justified application in science and contributed to is usefulness, it seems to me that it has hitherto appeared principally in the role of a variable quantity, which either grows beyond all bounds or diminishes to any desired minuteness, but always remains finite. I call this the improper infinite [das Uneigentlich-unendliche].
Georg Cantor
Source
Report...
In order for there to be a variable quantity in some mathematical study, the domain of its variability must strictly speaking be known beforehand through a definition. However, this domain cannot itself be something variable, since otherwise each fixed support for the study would collapse. Thus this domain is a definite, actually infinite set of values. Hence each potential infinite, if it is rigorously applicable mathematically, presupposes an actual infinite.
Georg Cantor
Source
Report...
Infinity, in its first form (the improper-infinite) presents itself as a variable finite [veranderliches Endliches]; in the other form (which I call the proper infinite [Eigentlich-unendliche]) it appears as a thoroughly determinate [bestimmtes] infinite.
Georg Cantor
Source
Report...
The potential infinite means nothing other than an undetermined, variable quantity, always remaining finite, which has to assume values that either become smaller than any finite limit no matter how small, or greater than any finite limit no matter how great.
Georg Cantor
Source
Report...
There is no doubt that we cannot do without variable quantities in the sense of the potential infinite. But from this very fact the necessity of the actual infinite can be demonstrated.
Georg Cantor
Quote of the day
There is no such thing in anyone's life as an unimportant day.
Alexander Woollcott
Georg Cantor
Creative Commons
Born:
March 3, 1845
Died:
January 6, 1918
(aged 72)
More about Georg Cantor...
Featured Authors
Lists
Predictions that didn't happen
If it's on the Internet it must be true
Remarkable Last Words (or Near-Last Words)
Picture Quotes
Confucius
Philip James Bailey
Eleanor Roosevelt
Letitia Elizabeth Landon
Popular Topics
life
love
nature
time
god
power
human
mind
work
art
heart
thought
men
day
×
Lib Quotes