Is 1 = 0.999... ? Really?

Look at the time that is mentioned below Jerkey’s post:

“Last edited by jerkey on Wed Jun 29, 2016 5:24 pm, edited 2 times in total.”

You posted after it. Look at the time that is mentioned above your post:

“by James S Saint » Wed Jun 29, 2016 5:48 pm”.

Strange!

Yeah 24 minutes seems like a lot of settle time required by a server.

James, you’re treating an infinite string as though it’s just a really, really long finite string (thus leaving a “last little bit”, presumably after the “last digit” at the “end” of the “endless” string…). That isn’t true. A really, really long finite string has a last digit, an infinite string does not. A really,really long finite string would indeed leave a “last little bit” left over, but we aren’t talking about a really, really long finite string, we’re talking about an infinite string. That distinction is crucially important.

And it was about 5:30 pm when I read that Jerkey edited his post. :wink:

I have never seen that on ILP before. :astonished:

In addition: the server does not “know” when the next poster is going to post. :wink:

The rule is that it is not possible to read that you edited your post when you did it before the next poster posted.

Realize that as they make machines more and more clever, machines begin to be able to do what humans would think impossible. :open_mouth: :evilfun:

:wink:

So could not the two impossibilities somehow have some sort of congruence?

No. That is what YOU are doing when you claim that there is a 0 “at the end once it gets to infinity”.

I am saying that because there is no end, the 9s must still be going - ALWAYS (true by definition). And thus never, ever becoming the string of 0s required for “1.000…”.

What two?

I was expecting that,James let me go back and recite from Your responses. Get back in a second

In Your response ending in ‘that clould never happen’ -5 of Your responses back in the forum, and the one two back, ending with ‘impossible’ - referring to machine intelligence.

It could never happen - is equivocal to - impossible

As per patterns, congruence and possibility.

The claim is that there are two decimal expansions for the number 1: a 1 with an infinite string of 0s after the decimal, and 0 with an infinite string of 9s after the decimal. Both are equivalent decimal expansions for the same integer. So there is no requirement that the 9s morph into a string of 0s, the string of 9s itself is equal to 1.

Multiple forms of the same value are common in math: 1/2 = 2/4 = 3/6 = 0.5 = .4999…

Jerkey, he simply means that the equation of 1 = 0,999… does at last not absolutely work: although the difference of both numbers becomes smaller and smaller, they can’t become equal, because there remains always a rest, an infinite small rest but a rest. So this equation works mathematically, of course, but that does not mean that it also works logically, thus philosophically. It is a solution for mathematicians but not for philosophers. One can always say that there is a rest that denies the equation.

This also indicates that mathematics and philosophy are two different disciplines, and history has shown that they have to be different disciplines.

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That is your false assertion that you keep claiming, yet haven’t provided any proof at all, whereas I have provided two proofs that you have yet to fault, but rather merely deny.

True, because you keep misstating it. Most recently, you claimed that for .999… to equal 1, at some point in the decimal expansion the 9s have to be replaced with 0s. That isn’t true, it not required, it’s not what anyone’s claiming. That claim is that .999… and 1 are equivalent decimal expansions of the same integer.

You accept that the limit as the number of 9s goes to infinity is 1, right?

The “limit” is the point that CANNOT be reached, but merely approached. There are many infinite series that approach 1. 1 is their “limit”. But the series are not at all equal to each other.

To be pedantic: Plenty of limits can be reached, it’s possible to have a finite limit.

So the limit goes to 1, so do we agree that if there were an infinite number of 9s, .999… would equal 1? If not, what do you mean by the limit?

With the limit, you can think of the approach as getting closer and closer to 1 (as you have explained using an infinite sum). So if the 9s are actually infinite, the value is as close to 1 as it’s possible to get. And that’s 1.

What about with 1/3, why is .333… not the proper decimal expansion?

It’s an ordinary geometric series and there is a formula for calculating its sum [ S=(a1)/(1-r)].
hotmath.com/hotmath_help/topics/ … eries.html

But apparently we are supposed to throw away hundreds of years of math, because James says so … #-o

Note : There is a formula for the sum of a finite number of terms of a geometric series. This formula can be easily verified.

Why should we think that the formula for the sum of an infinite number of terms, of the same series, is wrong? :-k

Arninius:

I see where James is comimg from, but my point is that it works both mathematically and philosophycally.