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J'Dona

Ending the 0.999~ = 1 debates

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Quote from Matt Matson: "The physical universe plays no role in deciding mathematical truths"

 

What if a system is 100% faultless and makes a mistake? It simply can not happen. If it did happen, then all mathematical theorems and laws of nature will fail. The physical universe is the ultimate test to mathematical constructs. They cannot contradict each other and both be correct.

 

The point I’m trying to explain is that a system with 99.999% certainty still contains a small amount of uncertainty while a system with 100% certainty has 0 uncertainty.

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Curios: thats the entire point, the 99.999% certainty would not contain any uncertainty and be equal to 100%.

 

Another example I can think of is a trans-planetary missile that is 99.999% accurate. When launching that missile to Pluto for example' date=' a tolerance between where it is aimed and where it will hit exists and is certain.

[/quote']

 

If it was 99.999% accurate they wouldn't say 99.999%. They'd say 100%. lol

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The point I’m trying to explain is that a system with 99.999% certainty still contains a small amount of uncertainty while a system with 100% certainty has 0 uncertainty

 

Does it? Give us the +/- number for that level of uncertainty.

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yah, and 0.0001 is not a number that exists, so you'll have a hard time giving an actual number.

 

funny how this thread is called "Ending the 0.999~ = 1 debates" since this debate will obviously not end no matter how many proofs showing that 0.999~ does = 1 :P are presented...

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Quote from Matt Matson: "The physical universe plays no role in deciding mathematical truths"

 

What if a system is 100% faultless and makes a mistake? It simply can not happen. If it did happen' date=' then all mathematical theorems and laws of nature will fail. The physical universe is the ultimate test to mathematical constructs. They cannot contradict each other and both be correct.

[/quote']

 

Do yourself a huge favor: Pick up an elementary textbook in mathematics and read it.

 

The point I’m trying to explain is that a system with 99.999% certainty still contains a small amount of uncertainty while a system with 100% certainty has 0 uncertainty.

 

And the point I am trying to explain is that your goofball notions of mathematics are rejected by those who work in the field.

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What's wrong Tom Mattson? Don't tell me you're letting the trivial debate get under your skin.

 

Please dont give any favours out to anyone but yourself.

 

Appreciated

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What's wrong Tom Mattson? Don't tell me you're letting the trivial debate get under your skin.

 

No' date=' not at all. In fact I'm more amused than anything else.

 

Please dont give any favours out to anyone but yourself.

 

You are posting on a message board that is devoted to science. That means that you can expect to have your mistakes pointed out, and you can further expect suggestions on how to remedy them.

 

Mathematics is an academic discipline that requires a great deal of hard work and dedication. There are people here who have done that hard work. When you post things that contradict what every authority in mathematics says about mathematics it sends the message that you think you know the subject better than they do, despite the fact that you clearly have not done the necessary hard work to understand it.

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Frankly, this thread has gone on long enough. Unless people decide to post some sensible, reasoned arguments then I will simply close the thread.

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The best argument against 0.999.... = 1 is

 

0.999.... will never equal 1.

 

You must go to infinity to make a geometric series -or any other proof- prove that 1 = 0.999.... But by infinity's definition it can never be reached, therefore 0.999... never equals 1.

 

You are never at infinity, you never have infinity in your hands to dividide by and you are never allowed to repeat a geometric series infinitely. You are treating infinity as if it is there for any fool to use.

 

Reenforcement - As x gets really really big (goes off toward infinity, *eye roll*) 1-(1/x) represents 0.999... but x is never infinity, so it is entirely inappropriate to do arithmetic at infinity.

 

And this is where we move on to calculus and thus math as a tool rather than a philosopher's play thing.

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Sorry, but that's nonsense.

 

An infinite series is per definition a sum of an infinite number of terms. The fact that there's no real infinity in 'nature' doesn't mean it doesn't exist in mathematics (since it does, and it only does so because we defined it somehow).

 

Infinite series surely exist and are very commonly used.

For example, we can define the number e as [math]\sum\limits_{n = 0}^\infty {\frac{1}{{n!}}} [/math]. If it's impossible to determine this infinite sum, then e wouldn't "exist".

 

You have probably once learned about rational and irrational numbers (which form the real numbers, together). A number was irrational if it has an infinite number of non-repeating decimals. So they never become periodic and they're not finite. It is also impossible to express these number as a fraction of two integers.

 

Rationals on the other hand, are the numbers which either have a finite number of decimals or which become periodic in their decimals. For example, 22/7 (which is an approximation for pi btw, pi being irrational itself) has the decimal expansion 3.142857142857142857..., or [math]{\rm{3}}{\rm{.}}\overline {{\rm{142857}}} = 3.142857...[/math]. Those last two numbers are merely other notations for 22/7 and its the same number 4 times, a rational one.

 

I assume it's clear that 0.999... has a repeating part as well (being just 9) and therefore, it has to be rational and thus it can be written as a fraction of integers. You tell me how that can be done, if 1 (=1/1=2/2 or whatever) isn't it.

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I think that (one of) the main arguments of the not-equal-to-oners (lol) is that infinity is not a number. Well, in a physical universe you can't have infinite of anything, it just doesn't work. However, like Tom Mattson said, mathematics is not dependent on the physical universe it's just a tool.

 

But besides that, if .999... does not equal one because it can't progress infinitley then its not a number at all, equal to one, or equal to anything for that matter.

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The best argument against 0.999.... = 1 is

 

0.999.... will never equal 1.

 

Can't you see that your premise and your conclusion say exactly the same thing??

 

I beseech the powers that be to lock this thread. It has descended into sheer crackpot nonsense.

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I've closed the thread, since it's gone on far too long now.

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