1 == 0.999...

[ihoss.com]

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

[Genesis F5]

Yeah, this is old. Sorry.

[Subway]

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

[Subway]

Oh by the way, just remembered a joke because of it:



Fredi

[MagnusVS]

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...

[Subway]

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

[silverx2]

it should read 1/3 = .3333~

and its a joke, aka haha heehee wink wink nudge nudge.

[yasunobu13]

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

How is it not a number? if 0.333... is not a number, then 1/3 isn't a number.

[Subway]

How is it not a number? if 0.333... is not a number, then 1/3 isn't a number.

1 is a number
3 is a number
/ is an operator

1/3 is math

Fredi

[yasunobu13]

1 is a number
3 is a number
/ is an operator

1/3 is math

If it's math, then it's an equation with a solution. Do apply that operator for me and tell me the result.

[silverx2]

flashkit has hit the nerd level.

[Subway]

Mission accomplished!

If it's math, then it's an equation with a solution. Do apply that operator for me and tell me the result.

You think every math equation has a solution that is a number? How about 1/0? Is infinite a number?

Fredi

[yasunobu13]

Mission accomplished!



You think every math equation has a solution that is a number? How about 1/0? Is infinite a number?

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.

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.

[Subway]

Ok, you win.

Fredi

[creativeinsomnia]

Hi, look at my new photo.

[random25]

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

[MagnusVS]

If 1/3=x then 1=3*x
What's x in that case? 0.333... is an exact solution.

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!

Anyway, 1 == 1. Nothing more, nothing less.

[yasunobu13]

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!

Anyway, 1 == 1. Nothing more, nothing less.

0.333... is shorthand for an infinite number of repeating 3's
So it is correct to say 1/3 = 0.333...

[random25]

Anyway, 1 == 1. Nothing more, nothing less.

Yea, and to prove it,
I will now go back to our machine shop and round all of the .999 measurements up to 1.

[silverx2]

i heard 1 = 2-1/1.. any truth to the rumor.