# 1=0.999... infinities and box of chocolates..Phliosophy of Math...

... 0.999... = 1

Is it a "real world" case or a purely mathematical case?
How does it relate to the "real" world?
Like 1 +2 = 3 it is math, but with applications to the "real world" where the IRS does more than that. I.e. tells you on your 1040 forms it is OK to call $4.49 =$4 but $4.51 =$5 so if it should arise, definitely in the real world of money 4.9999 = 5 even if not an infinite string of 9s.

Hi QQ.

When it comes to that question of maths vs reality, I unreservedly agree with Fednis48 when, in that other associated thread, he said:

Fednis48 said:
Math helps us describe reality. It is not the same as reality. ...

As to what the "0.9999..." example represents, from my observations of present and past discussions about this very thing, it appears that that example is only consistent/applicable to results/treatments within the axiomatic system where it arises as part of the conventions and assumptions therein. It is not intended, as far as I can gather, that it should be taken 'out of context' from the relevant maths-only construct/concept abstractions into the reality context as such.

Cheers.

Hi Fednis48, Billy T.

Thank you for stating clearly what I've been trying to get to with Undefined. Fractions - like any other mathematical constructs - can only reflect the real world up to a finite degree of precision. It's important to realize, though, that this is an entirely different issue from the nature of infinitesimals.

In my post to QQ just above (which alludes to already mutual understanding re this aspect), I already observed that we essentially have never really been in disagreement about that fundamental maths vs reality disconnect being a real thing and not just semantics. Ie, the already 'given' in all these discussions should be what has already been mutually agreed long since; to wit:

Fednis48 said:
Math helps us describe reality. It is not the same as reality. ...

Cheers.

Like 1 +2 = 3 it is math, but with applications to the "real world" where the IRS does more than that. I.e. tells you on your 1040 forms it is OK to call $4.49 =$4 but $4.51 =$5 so if it should arise, definitely in the real world of money 4.9999 = 5 even if not an infinite string of 9s.
Interesting reference...
Funny thing is in the banking industry I can guarantee you that the 1 cent in the difference between $9.99 and$10.00 can be a huge issue.
And I will also mention with 99.9999999....% certainty that playing the decimal "digit game" in stock trading, currency trading and other areas of "refined money business" is a massive area of interest for those in the high end of town.

Which leads to the issue of how "Probability Specialist" consider this 0.999... = 1 scenario... aka gaming and gambling...

Are the chances of correctly throwing the dice effected? [when looked at with such a powerful "statistical" microscope?
===
The more low value sales [ ie. by a supermarket] makes that are rounded up, to a given customer the more money the supermarket receives from the customer [ overall] so promoting small cash purchases that are rounded up those couple of cents soon add up. rather than selling fewer but larger purchases..

ie individual sales
$2.00 inc. round +2cents$2.50 round +3cents
$10.50 round +2 cents Total sale$15.00 rounding benefit 7cents instead of only a max of 4 cents if sold as one sale. marketing method gain = 3 cents per \$15.00

Hi Fednis48, Billy T.

In my post to QQ just above (which alludes to already mutual understanding re this aspect), I already observed that we essentially have never really been in disagreement about that fundamental maths vs reality disconnect being a real thing and not just semantics. Cheers.
I tend to think it is the term "disconnect" that is throwing people.. think of another term(s) such as "diminished real world relevance".. might help in modifying the angst that the word "disconnect" seems to generate. [as I think that it is being interpreted immediately as "fringe" raising crank alarm bells]

Hi rpenner.

Very interesting posts, thanks. Speaking of math modulo processes/operations/functions etc...

If q is prime and GCF(b,q) = 1 then $$b^{q-1} \; \textrm{mod} \; q \; = \; 1$$ (Fermat's little theorem) so q divides evenly $$b^{q-1} - 1$$ and so $$\frac{1}{q}$$ repeats in some factor of q-1 digits in base b.

But usually we describe the period as the smallest repeating segment.

http://en.wikipedia.org/wiki/Repeating_decimal#Fractions_with_prime_denominators

I would appreciate your comments on a longstanding observation of mine involving the 12 O'clock 'point' location in the circle of a 12-hour clock face where the end-point/location ("12" O'clock) of one 'round' is SIMULTANEOUSLY (in every sense?) the beginning ("0" O'Clock) of the next 'round'.

Can you elucidate the conventional axiomatic treatments/assumptions which the current maths brings to the observation/fact/situation that the "0"-is simultaneously-"12" sort of "super-position state" inherently involved/reflected in that aspect of the '12-hour Clock' modulo math case?

Your professional maths views/insights regarding this would be sincerely much appreciated, rpenner.

Hi rpenner.

Very interesting posts, thanks. Speaking of math modulo processes/operations/functions etc...

I would appreciate your comments on a longstanding observation of mine involving the 12 O'clock 'point' location in the circle of a 12-hour clock face where the end-point/location ("12" O'clock) of one 'round' is SIMULTANEOUSLY (in every sense?) the beginning ("0" O'Clock) of the next 'round'.

Can you elucidate the conventional axiomatic treatments/assumptions which the current maths brings to the observation/fact/situation that the "0"-is simultaneously-"12" sort of "super-position state" inherently involved/reflected in that aspect of the '12-hour Clock' modulo math case?

Your professional maths views/insights regarding this would be sincerely much appreciated, rpenner.
OMG that raises an interesting issue.. that does!

as time progresses how does the 0.999...=1 issue effect the clock?
do we just skip the
10.999.... o'clock moment and call it 11
11.999.... o'clock moment and call it 12

and consider all the 0.999... moments around the clock... [chuckle]

"Gosh where has all the time gone?"
or
"A clock with out any numbers on it's face"
-yeah crazy I know...
Yet the moment before the 0.999... is also a 0.999... moment ...and that applies all the way round the clock... so no time = no need for numbers to begin with [ chuckle ]
re: the brick gendanken

The philosophy of math question:
Does the use of infinity limits in math break the "smooth" continuum of movement [ time ]?

hmmmm......
The irony is that at any given moment eg t= 10am we are really referencing a zero duration point on the time line. so therefore exactly 10 am does not actually exist at all.

[unless you wish to allow absolute rest for a Planck moment]

I tend to think it is the term "disconnect" that is throwing people.. think of another term(s) such as "diminished real world relevance".. might help in modifying the angst that the word "disconnect" seems to generate. [as I think that it is being interpreted immediately as "fringe" raising crank alarm bells]

Hmmm. Yes, you could have something there, QQ. The 'kneejerk eliciting' potential attached to 'disconnect' is very high when that term 'hits the eye' of certain readers/respondents more driven by subjective emotional 'triggers' than dispassionate objective reading/response. I will in future seriously consider using some different term in like vein as you suggest there, QQ! Every little device/opportunity for 'calming of passion' helps in science discourse, hey? Thanks.

Hmmm. Yes, you could have something there, QQ. The 'kneejerk eliciting' potential attached to 'disconnect' is very high when that term 'hits the eye' of certain readers/respondents more driven by subjective emotional 'triggers' than dispassionate objective reading/response. I will in future seriously consider using some different term in like vein as you suggest there, QQ! Every little device/opportunity for 'calming of passion' helps in science discourse, hey? Thanks.
certainly worth a thought or two...

A question that has dropped out of all this for me:

Is relationship
0.777... to 0.888...
0.888... to 0.999...
the same as

0.999... is to 1
?

What relationship? The difference between them? The ratio?

This might help:
0.777... = 7/9
0.888... = 8/9
0.999... = 9/9
1 = 9/9

Hi Quantum Quack, handsa, Tach, rpenner, everyone.

This particular (immediately-below-quoted) exchange demonstrates where the problem may lay when trying to bring the discussion into the real physical world from the seemingly 'uncaring' mathematical assumptive world where the actual meanings of things like "point" and 'number 0" are unwittingly treated as a 'given' even though there is a fundamental question hanging over the competency of the current/conventional 'mathematical axiomatic' system to deal with these things at present stage of the mathematics formulation/practice:

Tach to handsa said:
handsa said:
You can divide a circle into three equal parts. Draw three radius from the center of a circle, which are 120 degrees apart. This will divide the circle into three equal parts.
This is one way of doing it, not the most elegant. How would you do it with a ruler and a compass only?

rpenner to someguy1 said:
someguy1 said:
That's harder than it looks. How do you account for each of the points on the boundary?
Those points have measure zero, so they really don't count, but a simple procedure of assigning each point to it's clockwise-adjacent arc will split the circle into N congruent parts.

Tach to rpenner said:
rpenner said:
Those points have measure zero, so they really don't count, but a simple procedure of assigning each point to it's clockwise-adjacent arc will split the circle into N congruent parts.
"Sharing" the endpoints by congruent arcs accomplishes the same result.

That incompetency is highlighted whenever (in the usual exchanges like that quoted above), there are effectively UNEXPLAINED assumptions made about the "0" and the "point" as for that 'proof of division into equal parts' in the case of a real 'pie' and not just an abstract 'circumference line for a circle. Now...

Consider the reality requirement for division of MD's real (not abstract) PIE; namely:

In the real world example of MD's PIE having a certain AREA in reality, the division has to INCLUDE the 'partition sector' VALUES so that they add together to the WHOLE starting area value.

Consider that such 'division' cannot be accomplished in reality, because:

There is no way in mathematics/reality to treat the CENTRE POINT which in handsa's 'method' is the "origin" point FOR the 'process' of division he suggested would do the trick.

Consider further the other 'methods' suggested earlier:

These too are EFFECTIVELY 'mute' on such matters as to what to do with the CENTRAL point (not circumferential points) in an AREA of points constituting a REAL pie DISC area (and not just the abstract notion of a 'circumference' LINE of POINTS isolation from that line's enclosed AREA which has to be SECTOR partitioned...in which case, as rpenner just pointed out...
rpenner said:
Those points have measure zero, so they really don't count,...

So, guys, this above observation, together with the earlier observations of such problematic "0", "superposition" and "origin points" as applies in the CIRCUMFERENTIAL ONLY context of MODULO MATHS in the 12-hour Clock context (please see my post to rpenner #146), CLEARLY demonstrates that conventional maths axiomatic treatments are not fully competent to EXPLAIN and consistently treat such "SINGULAR" cases where "0" and "point" is effectively associated with/constitutes NOT a "UNIQUE NUMBER" ON the number line, BUT SOMETHING ELSE entirely having contextual meanings/properties which BRIDGE ACROSS the limited treatments/domains of applicability of the current matyhs formalism as axiomatically constructed TO DATE.

Hence the need for further contextual axiomatic EXRENSION/REFINEMENT to ENHANCE the competency of the mathematics to handle such things that are BOTH/MANY 'things/values/states' SIMULTANEOUSLY as they REPRESENT TRANSITION states/points etc, and NOT just 'a number'. Hence the need for something like an INFINITESIMAL entity which can be associated with these states/transitions/values/superposition 'points' of CENTRE, ORIGIN, SINGULARITY characteristics/properties/effect IN REALITY and the MATHS both!

Then we may be able to obviate these constant Maths-versus-Reality cross-purpose arguments brought about by the current incomplete contextual capability of maths/physics systems/models to reflect/treat these things without 'outputting' such meaningless/unsatisfactory INCOMPLETE results as "UNDEFINED", or "INFINITY" or "LIMITED TO CHOSEN BOUNDARY CONDITIONS" etc.

Again, everyone, please read this post in conjunction with my earlier post to rpenner (#146) and consider carefully the subtle but important points I raised supported by examples/observations already familiar to us all by now. Please don't kneejerk; and do please read carefully, and without any emotional reaction at what you THINK you 'see' "at first blush".

No rush, guys!

I can wait until tomorrow or later for your replies. No sweat! So please maybe read this post (together with post #146) a couple times, and then sleep on it overnight and read it again. Then make your calmly considered and unemotional comments/responses. Thanks.

Hi Quantum Quack, handsa, Tach, rpenner, everyone.

This particular (immediately-below-quoted) exchange demonstrate where the problem lay when trying to bring the discussion into the real physical world from the seemingly 'uncaring' mathematical assumptive world where the actual meanings of things like "point" and 'number 0" are unwittingly treated as a 'given' even though there is a fundamental question hanging over the competency of the current/conventional 'mathematical axiomatic' system to deal with these things at present stage of the mathematics formulation/practice:

It is not clear why you needed to make such a long winded post only to demonstrate (again) your inability to understand a basic problem of geometry. Contrary to your nonsensical claims, any 8-th grader knows how to divide the circumference of a circle in three equal parts, using just a ruler and a compass.

That incompetency is highlighted whenever (in the usual exchanges like that quoted above), there are effectively UNEXPLAINED assumptions made about the "0" and the "point" as for that 'proof of division into equal parts' in the case of a real 'pie' and not just an abstract 'circumference line for a circle.

Rubbish. You call "incompetency" because you don't know the simple foundations of geometry.

It is not clear why you needed to make such a long winded post only to demonstrate (again) your inability to understand a basic problem of geometry. Contrary to your nonsensical claims, any 8-th grader knows how to divide the circumference of a circle in three equal parts, using just a ruler and a compass.

Rubbish. You call "incompetency" because you don't know the simple foundations of geometry.

*Sigh*

Tach, what did I say about NOT kneejerking, and taking time to read properly and sleep on it before making a CALMLY CONSIDERED and UNEMOTIONAL response?

It's the division of the AREA contained WITHIN (whatever abstract circumference line) that in reality is to be 'divided'.

As per MD's real PIE, and not some convenient/expedient 'abstraction' you wish to limit that reality division to for your own evasive/irrelevant unthinking purposes. Ok?

Now go away and READ PROPERLY and IN CONTEXT and THINK CAREFULLY before your next response to this. Thanks.

What relationship? The difference between them? The ratio?

This might help:
0.777... = 7/9
0.888... = 8/9
0.999... = 9/9
1 = 9/9
Sorry Pete for my impulsive post...The issue of a "smooth" continuum of movement [time] was the inspiration.

example:
1.(0).
dif = 0
0.(9)
dif = 0
0.8(9)
dif = 0
0.88(9)
dif = 0
0.888(9)
dif = 0
0.8888(9)

[therefore 1 - 0.8888(9) = 0]
and so on
the contention is:

if
1-0.999... = 0 then
all numbers are seriously effected.

if
1-0.999... = 0

and
0.999.... - 0.8999... = 0
and so on then extending the logic means that the ultimate difference between
9 and 8 is 0

because when you add all the differences up we get 0+0+0+0...

Using the basis of 1-0.999... = 0 as your "magnitude of difference" template.

the contention is:

if
1-0.999... = 0 then
all numbers are seriously effected.

You mean "affected", not "effected". How so?

if
1-0.999... = 0

and
0.999.... - 0.8999... = 0

What gives you this idea? Hint: it is wrong.

an so on then extending the logic means that the ultimate difference between
9 and 8 is 0

because when you add all the differences up we get 0+0+0+0...

GiGo.

It's the division of the AREA contained WITHIN (whatever abstract circumference line) that in reality is to be 'divided'.

As per MD's real PIE, and not some convenient/expedient 'abstraction' you wish to limit that reality division to for your own evasive/irrelevant unthinking purposes.

I read properly your long winded word salad, the 8-th grade algorithm that divides the circumference of the circle in three equal parts, divides the disc ("MD's pie") into three equal parts as well. Any person with a little knowledge of geometry could figure this out . Rather than incessantly spamming this forum, you should take an intro class to geometry.

You mean "affected", not "effected". How so?

What gives you this idea? Hint: it is wrong.

GiGo.
sure Tach... Take a tranq and settle down.. eh?

what's
0.(9) - 0.98(9) =
using your own limits logic it should = 0

what's
0.(9) - 0.98(9) =
using your own limits logic it should = 0

Nope, it is 0.01. Take a break from trolling and posting rubbish and see if you can prove it all by yourself.

Nope, it is 0.01. Go away from trolling and see if you can prove it all by yourself.
so are you saying that 0.9899999999999999999999(9) is a special case of infinity and that it doesn't equal 0.999999999(9)?

Comparative case:

if
9.99(9) = 10
then
9.899999999(9) = 9.999(9) = 10

If I am correct, then math needs the infinitesimal more than it realizes!