Peanuts by Charles Schulz for October 07, 1965
October 06, 1965
October 08, 1965
Transcript:
Sally watches as Linus writes and says, "Keep in mind that a numeral stands for a certain number of objects . . ."<BR><BR> Linus says, "Now, when you count what you are doing is matching elements one to one with a set of counting numbers . . ."<BR><BR> Linus continues, "In a set of numbers, the last numeral matched to that set is the cardinal number . . ."<BR><BR> Sally says, "There's a good program on tv tonight at seven o'clock."<BR><BR>
m.l. about 12 years ago
Stormwyrm over 3 years ago
One reason why mathematicians think of counting in that rather convoluted way Linus describes is that it allows them to reason about infinity. For instance, it turns out that while it seems that there should be “more” fractions than there are integers, it turns out there are lots of ways to match all possible fractions (rational numbers) one to one with all the integers, and so you could argue that there are just as many integers as there are fractions! However, it seems that there are somehow more real numbers than integers, in the sense that there is no way that you can match all of the real numbers one to one with all the integers.