However, this MUST be brought to light.
While visiting the Wikipedia site, oh, about 5 minutes ago, I noticed the "Featured article of the day", which is about the number 0.999..., which theoretically trails on indefinitely.
However, it says that, in most textbooks and by most mathemeticians' standards, 0.999... is equal to 1.
This is apparently common knowledge, folks, and can be PROVED in a variety of ways.
I am, therefore led to the following two assumptions:
1. Mathematicians have way too much time on their hands. Proving that 0.99... equals 1? Einstein at least made up something theoretically useful. Theoretically.
So, have mathematicians run out of things to theoretically prove? Or, are they just slacking off?
2. Math, as we know it, is wrong. What other explanation could there be? When one number that is so obviously different from another number is equal to the second number, and this can be PROVEN, what does that tell us about the innocuous number system that we teach to our students every day? It must be flawed. In my opinion, 0.999... can aspire all it wants to be 1, but it will NEVER be equal to 1. NEVER! Instead of trying to put shackles on 0.999... and try to make it and 1 equal, we should embrace its innate differences and love it for what it truly is.
I will fight to defend the honor of 0.999... and 1 just as I would fight for... well...
1 comment:
You may indeed think that mathematicians have too much spare time, coming up with such abstract notions - that is, of course, a matter of opinion. I can assure you, 0.999... = 1 is one of the less abstract things that can be shown in mathematics! Indeed, many people might hear about imaginary numbers (which include such oddities as the square root of -1) and immediately assume they have no actual use in the real world - quite on the contrary, complex analysis (which uses said "imaginary" numbers) has been used in very practical fields, including physics and engineering. Indeed, we even use them at my work (I work for a dewatering company), and to great effect! Similarly, other abstract, seemingly useless branches of mathematics have lead to insight that manifests itself in practical uses.
And of course, mathematics is not "wrong" about this. I suggest you read the Wikipedia article for some of the proofs, and really give it some thought. All that's happening is that a number is being recognised as having more than one decimal representation - indeed, 0.5 can also be represented as the fraction 1/2 and nobody would complain about that!
John Graham
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