Do you think 0.9~ is exactly equal to 1?

Post by **Hermit** » Tue Mar 24, 2009 2:50 pm

Revealing my masochistic side here.

This is what I said at RDN on the subject:

I divide one cake into three equal slices, finshing up with

1/3 of a cake and
1/3 of a cake and
1/3 of a cake.

Putting the slices back together, I have 1 cake again (ignoring the crumbs).

If I re-express 1/3 as 0.3~ (*) and add the three slices together I finish up with 3 times 0.3~ slices making up 0.9~ of cake, which equals exactly 3 times 1/3, that is to say exactly 1 cake. (I can safely ignore the crumbs, seeing this is a mathematical abstraction of a real world experiment.)

So, I say: yes.

Incidentally, with 446 votes the poll at RDN currently stands at 56% for the affirmative and 44% for the negative.

(*) and that should basically be self evident. If you disagree, try your skills of long division on this and let me know as soon as you have reason to believe that you will run out of 3s.

devogue · Post by **devogue** » Tue Mar 24, 2009 3:02 pm

Seraph wrote:Revealing my masochistic side here.

This is what I said at RDN on the subject:

I divide one cake into three equal slices, finshing up with

1/3 of a cake and
1/3 of a cake and
1/3 of a cake.

Putting the slices back together, I have 1 cake again (ignoring the crumbs).

If I re-express 1/3 as 0.3~ (*) and add the three slices together I finish up with 3 times 0.3~ slices making up 0.9~ of cake, which equals exactly 3 times 1/3, that is to say exactly 1 cake. (I can safely ignore the crumbs, seeing this is a mathematical abstraction of a real world experiment.)

So, I say: yes.

Incidentally, with 446 votes the poll at RDN currently stands at 56% for the affirmative and 44% for the negative.

(*) and that should basically be self evident. If you disagree, try your skills of long division on this and let me know as soon as you have reason to believe that you will run out of 3s.

Isn't "1" just a handy way of summing up that infinity of "3"s?

Post by **Feck** » Tue Mar 24, 2009 3:04 pm

As a normal human being (I do not speak Math) three thirds is one, and 22/7 works for me too.

devogue · Post by **devogue** » Tue Mar 24, 2009 3:06 pm

mrenutt4 wrote:As a normal human being (I do not speak Math) three thirds is one, and 22/7 works for me too.

I'm a 24/7 kinda guy myself...

This is maths in the realm of philosophy. It scares me.

Post by **Xamonas Chegwé** » Tue Mar 24, 2009 3:12 pm

It definitely IS equal to 1. Here's the most elegantly simple proof I know.

Let x = 0.9999... (A)

Therefore 10x = 9.9999... (B)

Subtracting A from B gives 10x - x = 9.9999... - 0.9999...

Which resolves to 9x = 9

And dividing both sides by 9 gives x = 1

QED.

Post by **JimC** » Tue Apr 14, 2009 9:52 am

The issue here is the difficulty the human mind has in interpreting the concept of an infinite number of decimal points.

XC's proof is both correct and straightforward.

What this should teach us is that infinitely recurring decimal places are mathematical objects which defy our normal, common sense view of decimal operations, precisely because that the qualifier "an infinite number" puts them into a separate category.

In addition, the sophisticated part of the maths comes from the application of limit theory to geometric series where r < 1

rationalia.com

Do you think 0.9~ is exactly equal to 1?

Do you think 0.9~ equals exactly 1?

Do you think 0.9~ is exactly equal to 1?

Re: Do you think 0.9~ is exactly equal to 1?

Re: Do you think 0.9~ is exactly equal to 1?

Re: Do you think 0.9~ is exactly equal to 1?

Re: Do you think 0.9~ is exactly equal to 1?

Re: Do you think 0.9~ is exactly equal to 1?

Who is online