This is another version of the last post, which proves math is hard. I can't figure out how to type the line over the 9 to make "POINT NINE REPEATING" so I will write it like this: .999999.....
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(If I start with this)
X = .99999....
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(And then I multiply each side by 10)
10X = 9.99999....
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(Since X = .999999... that's how much I will subtract from each side to reduce)
9X = 9
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(Now I divide each side by 9 to reduce again)
X = 1
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But earlier X = .9999....
So does this prove 1 = .999999......?
I wish I'd have known about this in school so I could have explained the futility of learning math. That would have saved a lot of time. Maybe my teacher would have said, "Yes, go out and play until we fix math. No sense in teaching it until we get all the bugs worked out."
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I dreamt recently I was back in High School and there was a Pop-Quiz, for which I was completely unprepared. I stood up and announced to the Teacher: "I just don't see how this directly pertains to my life." and walked out.
ReplyDeleteMan~! I sure have some ca-honies on the Dreamscape~!
This is why I draw!
ReplyDeleteLysdexicuss, Ha ha!
ReplyDeleteWhen I was in 6th grade I asked my Social Studies teacher why we needed to know Social Studies and she couldn't tell me.
Willy, Well it's working so keep doing what you're doing!
Pretty nice. :) I just thought of this intuitive proof which is easy to visualize:
ReplyDeleteTake a string that's 1 foot long and cut it in 10 pieces. Take 9 pieces and set them aside in a pile.
The tenth piece, cut it into 10 more pieces (where each part is 1/100 the size). Now set 9 of these peices in a pile.
And the last piece you just cut, cut this string into 10 more pieces (now each part 1/1000 the size).
Imagine this goes on without end.
Regardless of how many parts, the sum of the parts must still equal the original length. Since we aren't throwing any pieces away. So the length of all the cut strings will equal 1 foot. So,
1 = 9/10 + 9/100 + 9/1000 + ...
or in decimal notation,
1 = .999...
IOW, it's two ways to look at the same length (as a infinite sum of parts). Course, in the real world if we are cutting something, that would probably shorten them all a bit. :)
That's a good way to think about it. I guess it's like making a verb out of a noun. The number is constantly changing so it's like it's alive. That's what makes it weird to try and pin down long enough to add. By the time you've added it, it's a different infinite number.
ReplyDelete