The General Questions forum is for questions with factual answers. Speculation about government agencies in Utah based on nothing more than time stamps is not only off topic for this thread but is also outside of the scope of this forum. Please stick to the mathematical topic at hand and do not attempt to hijack this thread with any further discussions of government agencies, NSA or otherwise.
The Pit in this case refers to the BBQ Pit forum, which is the forum in which you may insult posters (basically, you can let the flames fly, hence the name, though there are restrictions).
You would do well to tone back the confrontational nature of your posts. It might be a good idea to stop posting for a bit and read a few of the FAQs and other posts here so that you can get a better idea of what is and is not acceptable here.
No warnings issued.
If you wish to discuss the NSA and other government functions, do so in another thread in the appropriate forum.
If you have problems with other posters, take it to the Pit.
This isn’t even the slightest bit true. There is a world of difference between a scientific theory and a mathematical proof. The former may be contradicted by experiment and observation, which may in turn require the theory to be modified or abandoned. The latter, if rigorous, is simply true.
You have used the term “scientific method” a number of times now. Either you don’t understand what it means or you are being deliberately obtuse, because it simply has no bearing on a mathematical proof.
In post #1462The Hamster King once again lays out an elegant proof that 0.333… = 1/3. It’s very simple to follow. Once we have that result then the rest of the proof that 0.999… = 1 follows trivially (multiply each side by 3).
Unless you can indicate where you disagree with The Hamster King’s proof then the only conclusion to be reached is that you are not serious in your endeavours.
My objective is to, via other operations defined by the axioms, see how they lead to a contradiction within the set such as an equation which is clearly erroneous…ie 2 > 3 etc.
The process is iterative and involves substitution and application of the axioms.
So again, I don’t understand what you are saying, yes I agree that they are axioms and are used in the process of showing that they lead to an obvious error within the set.
If the equivalency leads to an error, ie I go from an equality to an inequality, then clearly there is a problem with the axiom.
No, Cognitive Tide, they are not axioms of the set (why set?), they are consequences of the axioms governing real numbers.
The GREAT news for you is that if you can show that either of those two consequences lead to a contradiction (2>3 or other such) then you will have shaken mathematics to its very core and not just demonstrated the falsehood of a somewhat modest theorem (viz 0.999… =1).
Your input would be greatly appreciated. For starters please multiply out [.0111…]^2
via a multiplication algorithm and let me know if you get a conflicting result…else the proof is
valid.
To Crimson Tide
Ahhh long division. So little used these days. And such a useful algorithm. It enables a person to convert between the fractional representation of a number and the decimal representation of a number – using nothing more than pen and paper.
For example, I just used a pen and paper to show that the fraction 33/25 = 1.32
It is a bit strange to think that the same number might have more than one representation. But I am confident that 33/25 does in fact equal 1.32. After thinking about this for a while, I am comfortable with the notion of having many representations of the same number.
1/2 = 3/6 = 0.5 = 0.4(oct)
I am delighted to encounter a kindred spirit who appreciates both long division and recursion. So, I tell you what…
Why don’t you do a bit of long division and work out the decimal representation of 1/3. I am really interested to know since it might resolve this silly 0.9999…=1 thing once and for all.
I have started. I am up to the 574th decimal place so far and all I got is threes.
Just pen and paper. We may as well do it old school – the same as I did with 33/25.
And when you have finished, I invite you to report back to us your findings. There are a bunch of professional mathematicians here who eagerly await your response.
In particular, I would really like to know the exact decimal place where the answer deviates from 0.3333… It must be somewhere after the 574th decimal place but I am not sure that it is coming soon.
I also agree with you that the empirical world and mathematics should not be separated. So when you reply with your answer, I would love you to post a photo (or video) of your working so that we can all see the decimal place that differs.
I’m a carpenter, so I can race you in base 12 arithmetic. I do my own bookkeeping, so I could probably show you a few ways to save on taxes.
… and I know there are nine axioms that define a vector space. I know that real numbers are a vector space. Therefore, there are only nine axioms that “govern” the real numbers … no more, no less.
You seem to be taking liberties with this established principle.
I can certainly post as many finite iterative steps that you want of this by giving you a flash video which you can watch from here till the day you die. Needless to say though
if you decide to stop and believe the answer you will need to make a “pattern recognition leap of faith”
If that was directed at me then all I have to say is that was amazingly quick. And I would love to see your working. I am on to my seventh sheet of paper here and am still only up to the 693rd decimal place.
That said, I am sure I don’t understand your notation. Again, care to post a photo of your working? I can only assume you are doing long division using a different algorithm from me.
I wouldn’t need that many decimal places to stop, but we all have to make our own choices don’t we…the point is, you CANNOT discard the remainder. Its not just a sprig of parsley you know.