Comments on: Another from This Week’s WEedies! http://micahtillman.com/2008/06/06/another-from-this-weeks-weedies/ Philosophy, Politics, Religion, Etc. Mon, 01 Dec 2008 23:26:46 +0000 http://wordpress.org/?v=2.6.3 By: Micah Tillman http://micahtillman.com/2008/06/06/another-from-this-weeks-weedies/#comment-2582 Micah Tillman Fri, 06 Jun 2008 20:43:34 +0000 http://micahtillman.com/?p=427#comment-2582 <blockquote>infinity isn't a number at all.</blockquote> Indeed! Which is fun. And all the logical/arithmetical problems with dealing with division by zero and infinity and what not are fun too :-)

infinity isn’t a number at all.

Indeed! Which is fun.

And all the logical/arithmetical problems with dealing with division by zero and infinity and what not are fun too :-)

]]> By: Andrew Stevens http://micahtillman.com/2008/06/06/another-from-this-weeks-weedies/#comment-2581 Andrew Stevens Fri, 06 Jun 2008 19:48:02 +0000 http://micahtillman.com/?p=427#comment-2581 Oops, didn't see your PPS. It is true that we can define division by zero on the non-negative reals and extend the non-negative number line to include infinity, but if you do that, you're leaving subtraction undefined in many places since negative numbers don't exist. (By the by, including infinity in the non-negative reals is also a problem since infinity isn't a number at all.) Oops, didn’t see your PPS. It is true that we can define division by zero on the non-negative reals and extend the non-negative number line to include infinity, but if you do that, you’re leaving subtraction undefined in many places since negative numbers don’t exist. (By the by, including infinity in the non-negative reals is also a problem since infinity isn’t a number at all.)

]]> By: Andrew Stevens http://micahtillman.com/2008/06/06/another-from-this-weeks-weedies/#comment-2580 Andrew Stevens Fri, 06 Jun 2008 19:45:12 +0000 http://micahtillman.com/?p=427#comment-2580 Micah, what value f(x) takes depends on whether we take the limit from the right or from the left. If we take it from the right, it approaches infinity, but if we take it from the left, it approaches negative infinity. Thus, when x=0, the answer seems to be both infinity and negative infinity, implying that the two are equal. The two are not equal, therefore division by zero is undefined. Micah, what value f(x) takes depends on whether we take the limit from the right or from the left. If we take it from the right, it approaches infinity, but if we take it from the left, it approaches negative infinity. Thus, when x=0, the answer seems to be both infinity and negative infinity, implying that the two are equal. The two are not equal, therefore division by zero is undefined.

]]> By: Micah Tillman http://micahtillman.com/2008/06/06/another-from-this-weeks-weedies/#comment-2579 Micah Tillman Fri, 06 Jun 2008 18:21:06 +0000 http://micahtillman.com/?p=427#comment-2579 PPS And I meant: "as x approaches zero from the positive side," since the number of non-WEedy sentences in a WEedy-winning piece is always either positive or zero. *grin* UPDATED PPS
And I meant: “as x approaches zero from the positive side,” since the number of non-WEedy sentences in a WEedy-winning piece is always either positive or zero.
*grin*
UPDATED

]]> By: Micah Tillman http://micahtillman.com/2008/06/06/another-from-this-weeks-weedies/#comment-2578 Micah Tillman Fri, 06 Jun 2008 18:18:34 +0000 http://micahtillman.com/?p=427#comment-2578 PS My Calc III prof would always tell us that if we divided by zero, the world would explode. So we better not do it. :-) PS
My Calc III prof would always tell us that if we divided by zero, the world would explode. So we better not do it. :-)

]]> By: Micah Tillman http://micahtillman.com/2008/06/06/another-from-this-weeks-weedies/#comment-2577 Micah Tillman Fri, 06 Jun 2008 18:10:47 +0000 http://micahtillman.com/?p=427#comment-2577 Let f(x) = 1/x What value will f(x) approach as x approaches 0 (zero)? Let f(x) = 1/x

What value will f(x) approach as x approaches 0 (zero)?

]]> By: Andrew Stevens http://micahtillman.com/2008/06/06/another-from-this-weeks-weedies/#comment-2576 Andrew Stevens Fri, 06 Jun 2008 18:04:34 +0000 http://micahtillman.com/?p=427#comment-2576 2/0 doesn't equal infinity. Division by zero is illegal in Iowa (and probably D.C. as well) and the answer to the equation is undefined. If we take n/0 to be infinity then this implies that zero times infinity equals every number, which would mean all numbers are equal. 2/0 equals infinity is a tempting conclusion, but not correct. (It also implies that positive infinity is equal to negative infinity, which causes some problems in analysis.) 2/0 doesn’t equal infinity. Division by zero is illegal in Iowa (and probably D.C. as well) and the answer to the equation is undefined. If we take n/0 to be infinity then this implies that zero times infinity equals every number, which would mean all numbers are equal. 2/0 equals infinity is a tempting conclusion, but not correct. (It also implies that positive infinity is equal to negative infinity, which causes some problems in analysis.)

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