Brain Burp Rounding??
michael brown email (remove spam text)
----- Original Message -----
From: "David VanHorn" <CEDAR.NET> dvanhorn
To: <MITVMA.MIT.EDU> PICLIST
Sent: Saturday, June 02, 2001 9:57 PM
Subject: Re: [OT]: Brain Burp Rounding??
> As you expand the sequence, the difference becomes small, but it is never
> You claim 1 = 0.9...
> Is it then true that 1(inf) = 0.9...(inf)?
> There may be a rule which says so (Which I suspect exists to avoid ugly
> problems in calculation), but you're not going to convince me that a
> which is "less than 1 by an infinitely small amount" is equal to 1.
> Next, you'll want to sell me 5 pounds of potatoes multiplied by the Sqrt
> -1 :)
I'm with Dave on this one. Sqrt of -1 = i "i" - that amazingly
ridiculous, non-existant value that allows mathematicians to continue on
creating even more ridiculous mathematics coming up with answers that don't
(can't) exist. Sort of like "e" the fascinating irational number that
somehow ocupies an exact position on a number line. Where as pi is a
supposedly "irrational" number easily represented as a fraction (which by
definition makes it rational) as in pi = C/D where C is some number
representing circumfrence and D representing diameter of a circle. You
cannot use infinity in an equation and expect any sanity in the result.
However, we are supposed to accept these things and then also believe that
you cannot divide by 0 (answer is undefined even though the real answer
should be infinity). Since division is nothing but repetive subtraction,
you can easily prove (using a pic ;-D ) that dividing by 0 is infinite and
not "undefined". Look Dave its true 1=2 ;-)
a = x [true for some a's and x's]
a+a = a+x [add a to both sides]
2a = a+x [a+a = 2a]
2a-2x = a+x-2x [subtract 2x from both sides]
2(a-x) = a+x-2x [Factor left side]
2(a-x) = a-x [Simplify right side]
2 = 1 [divide both sides by a-x]
Of course we can't divide by zero, which is precisely what happens in the
last step. Back to the .999 rpt.=1 arithmetic with infinity is NOT allowed,
because infinity is not a number. And, just like our little puzzle, we get
answers that make no sense.
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