Meh, I can't argue with you. You are probably right (You've afterall made it through college already ). I see I have so much to look forward to in higher math.

Olaaaf wrote:Divide 1 by 3 (or 1 by 9, this is the same logic).
The calculus will loop and you'll find 0.333... an infinity of 3.

The number we represent by 0.333... IS a rational number (it is 1/3), but not a decimal number. A decimal number has a finite number of decimals.

Any number with infinite recurring sequence of decimals is rational.

Have you done university mathematics? No.

Thank you.

@ poisson:

It is a complicated issue, further compunded by the fact that the human brain is unable to really comprehend infinity.

Thomas1134 wrote:
Have you done university mathematics? No.

Thank you.

Well, yes. Yes I did.

And what did I say that could make you think otherwise?
Did university mathematics teach you that "I've done study so I'm right" was a valid argument? I doubt so.

A number with an infinite number of decimals is not a decimal number. And a decimal is always a rational.
And I can't write a proof here and now (the one I have been taught uses properties of the Euclidean division and is fairly long), but any number with recurring decimals is a rational.

Completely wrong.

Please tell me how recurring decimals are not decimals.

On the other hand, surds are irrational because they cannot be displayed as a fraction.

Well, there may be a translation problem from my part here.

English is not my mother tongue, and where I live, decimal representation is not the same as decimal number.
Any real number has a decimal representation. What we call decimal number is limited to decimal fractions, numbers that can be written as fractions with a power of 10 denominator.

Thus, we don't call surds decimal.

This could explain that.

Ah right.

In Western Europe and America, number is a decimal if it is a rational number.

Since 0.999... is a rational number (it can be represented as a fraction and has a repeating decimal), it is considered to be a decimal as well as 9/9 or 3/3.

Thomas1134 wrote:
In Western Europe and America, number is a decimal if it is a rational number.

Well, not all Western Europe it would seem. I'm French, and apparently this definition of "decimal numbers" is used in Spain too.
We even define the "set of decimal numbers", noted "D", which is a subset of Q and of which Z is a subset.
I didn't know this term didn't have the same meaning outside of a couple countries.

Useful to know, there are such things as cultural differences in Mathematics it seems

Thomas1134 wrote:

Jetboy109 wrote:Yes, it does equal one, for several reasons:

1. 1/9=0.1111111…, 2/9=0.222222222…, 3/9=0.33333333…,…8/9=0.8888888888… So, if 0.8888888888 is 8/9, and 0.111111… is 1/9, and 1/9 + 8/9=9/9=1, 0.888888888… + 0.111111111…=1, by the transitive property of equality. However, when one adds up the terms, one discovers that 0.99999999999…=1

Entirely correct.

I'm flattered.

Olaaaf wrote:
Problem is some people assume there are different levels of infinity, and that some things are "more infinite" than other. That's not the case. Something is finite or infinite, there's nothing in between.

Aren't there, though? Like ℵ*0?

And about what's rational and what isn't, I'm pretty sure that if it can be represented as a fraction of two integers, it's rational. However, the decimal thing is just another example why it would be better to switch to a base-twelve system.

Olaaaf wrote:

Thomas1134 wrote:
In Western Europe and America, number is a decimal if it is a rational number.

Well, not all Western Europe it would seem. I'm French, and apparently this definition of "decimal numbers" is used in Spain too.
We even define the "set of decimal numbers", noted "D", which is a subset of Q and of which Z is a subset.
I didn't know this term didn't have the same meaning outside of a couple countries.

Useful to know, there are such things as cultural differences in Mathematics it seems

Realy? Odd, considering that I know several French scientists who use our system.

Or maybe that is because our system (the British and American system) is the official international system.

You know, after pondering this question with the logic found in my brain, I have concluded this:

0.999... = 1

And then I realized:

Why should I care?

0.999 will never equal one. it will be so incredibly close, but not close enough.

You could add .(any number of zeroes here)1 to any part of it, and it will equal one.

ok let put it this way
in fraction then it doesn mean 1
if it not in fraction then it will not equal 1
9/9 =9/10
i think (making it up lol)
but still
3/3 equal 0.99999999999
you see 1 third is unbalanced
so 3/3 will forever equal 1
the number 3 is and always will be unblanced

http://qntm.org/index.php?pointnine

This site convinced me.

eSCSi wrote:http://qntm.org/index.php?pointnine

This site convinced me.

kinda what i was talking about

Strictly mathematically, 0.(9) is less than one. It's never >1.