1 + 1 + 1 = ?

[keelanz]

As far as I can see, it's a perfectly accurate metaphor; I'm not sure why you disagree. You can never exactly express a third using decimal numbers; you can with fractions. Also, what's pretentious about calling the universe "the universe"?

I'm well aware of the different number systems. However, since introducing all that extra information wouldn't do anything to help the attempted simplicity of the explanation, I refrained from giving it. Also, since it might not have been obvious from my previous post, I was responding to the following:

 

 

 

However, I might have misinterpreted the meaning; the way I understand it, and for me the post is not clear enough to be completely sure, the author was saying that numbers with infinite decimal places are "unreal". I was attempting to point out that there is a way to represent them finitely and thus helping the author accept their "realness", evidently not doing a great job of conveying that either.

 

A piece of trivia, which you might already know, not even the complex numbers occupy the highest level; see quaternions, octonions and sedenions.

 

 

keelanz: What numbering system would that be? The naturals?

 

Binary

[Shadow]

You're confusing number system with numeral system. The number systems are the different sets of numbers, ie. the naturals, the integers, reals etc. Binary, ternary, hexadecimal etc. are called numeral systems (similar in name, but completely different in meaning). But to answer you're question, if you're asking if 1/3 can be represented in binary, it can, but you get the same problem you would in decimal; the representation would again be infinitely long. Alternatively, you could the same fraction notation we use with decimal numbers to represent one third as [math]\frac{1_2}{11_2}[/math] but I've never seen that done before. Or, you could use the ternary numeral system to represent one third finitely as [math]0.1_3[/math]. Another example of how the finiteness of a representation depends entirely on the rules of representation we choose (ie. different number/numeral systems). I hope that last sentence makes sense.

Edited April 21, 2011 by Shadow

[soundoflight]

if zero has no value and we must have the sum of 1+ before getting to the sum of 2 then how do we arrive at the value of 1.

[DrRocket]

if zero has no value and we must have the sum of 1+ before getting to the sum of 2 then how do we arrive at the value of 1.

 

Exactly the same way that if you start with an empty plate and then put a pea on it, you now have one pea.

 

Get a copy of Landau's Foundations of Analysis and see all of the usual numbers built from just the Peano Postulates.