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This is very old, but I haven't heard about it before.
1 == 0.999...
It can be proven in two ways:
1
1/3 = 0.333...
1/3 * 3 = 0.333... * 3
1 = 0.999...
2
x = 0.999...
10x = 9.999...
10x - x = 9.999...- 0.999...
9x = 9
x = 1
Sorry if this has been posted before, but I couldn't find it (The search here is not good, it never finds anything, so it might be that I missed it).
If you don't believe me, have a look here
Yeah, this is old. Sorry. :D
1/3 != 0.333....!!!
0.333... is not a number! 0.333 is, but not 0.333...
As it isn't a number, you can't do math with it.
Fredi
Oh by the way, just remembered a joke because of it:
http://imgs.xkcd.com/comics/e_to_the_pi_minus_pi.png
Fredi
I absolutely agree with Fredi. 1/3 != 0.3333333...
Of course you can do math with it, but to say that 1/3==0.333... is like saying that 0.5 == 0.4999999 and prove from that that 50==49.999...
Ok, that's an even better explanation. :)
But I stand by my comment: 0.333... is not a number in the same way as "infinite" is not a number, it's just philosophy or (I just made that word up) metamath.
Fredi
it should read 1/3 = .3333~
and its a joke, aka haha heehee wink wink nudge nudge.
How is it not a number? if 0.333... is not a number, then 1/3 isn't a number.Quote:
Originally Posted by Subway
1 is a numberQuote:
Originally Posted by yasunobu13
3 is a number
/ is an operator
1/3 is math
Fredi
If it's math, then it's an equation with a solution. Do apply that operator for me and tell me the result.Quote:
Originally Posted by Subway
flashkit has hit the nerd level.
Mission accomplished!
You think every math equation has a solution that is a number? How about 1/0? Is infinite a number?Quote:
Originally Posted by yasunobu13
Fredi
The division operation is defined on all rational numbers except for when the divisor is 0 in which case the operation is undefined. Last I checked 1 and 3 are rational and non-zero.Quote:
Originally Posted by Subway
If 1/3=x then 1=3*x
What's x in that case? 0.333... is an exact solution.
The equation y = 1/x is a continuous function for x > 0. If 1/3 is undefined then y=1/x has no solution for x=3,6,7,9,11,13,...
How about this, the problem only occurs due to the base numbering system (base 10). If we change the problem to base 3 instead then the issue is
1/3 => 1/10
You agree that 1/10 has a solution of 0.1 correct? Change 0.1 in base 3 back to base 10 and you get 0.333...
Did a change of base of a number create a non-number here? That would make no sense.
Ok, you win. ;)
Fredi
Quote:
Originally Posted by yasunobu13
1 does not equal 0.999...
Keep running those 9s out infinitely and you are still not at 1.
Have you never seen Carl Sagan explain infinity?
Oh yea, and OLD!1
If you can place infinite amounts of 3'ers behind. The most correct way is to say that 1/3 == 1/3 and that's it!Quote:
Originally Posted by yasunobu13
Anyway, 1 == 1. Nothing more, nothing less.
0.333... is shorthand for an infinite number of repeating 3'sQuote:
Originally Posted by MagnusVS
So it is correct to say 1/3 = 0.333...
Yea, and to prove it,Quote:
Originally Posted by MagnusVS
I will now go back to our machine shop and round all of the .999 measurements up to 1.
i heard 1 = 2-1/1.. any truth to the rumor.