Mathematical Theory (controversy!)

For anyone who thinks that an infinitely recurring number can simply be redefined as another number, I ask this question:

Does PI (3.14159 etc ) which never repeats = 3.141.... (which is the same accuracy as the original question)?

I hope for the future of engineering that the answer is a resounding no!

There is a difference in the .999_ = 1 and the never-ending Pi. The Pi equivalent of that same theorum is

Pi = pi +/- 0.0_1, with the 0 repeating to infinity. It's the negligible space at the tail that throws in the whirlygig. .00059 is not negligible.

If they are not the same, I would like to see your disproof of the simple algebraic proof from my first post, and your disproofs of the numerous other proofs on the link I provided.

Or if they are really not the same, then what is the result of this expression?

1 - .999...

After all, if they are different, then the difference between the two must be some non-zero value.

Or look at this variation or the proof:

1/3 = 0.333...

so 3*(1/3) = 3*0.333... = 0.999...

since 3*(1/3) = 3/3 = 1,

then 1 = 0.999...

Finally, consider the following axiom:

Q: How many mathematicians does it take to screw in a lightbulb?

A: 0.999999....

This is definitely going to be my last post on this thread because I am getting an ache from having my tongue in my cheek for so long 😛

Are you really that confident of your working here ?

showing two different notations, one of which is an approximation and saying they are the same does not really constitute a proof does it?

Yes it is a non-zero value, but I do not have the symbology to write it down, however that does not negate it's own reality.

Again, just writing different numbers as equal and multiplying them by 3 does not prove anything to me. 0.333... is an approximation of 1/3, not an equality.

Agreed, it can be considered to be "equal enough" in most circumstances, but it needs to be accompanied by a degree of accuracy statement.

A: Show me how they got into the light bulb!

Seriously, I will not post again to this thread because I do not want to get into a war over this - everything I have said is just my opinion and I was only joking when I said that anyone who disagreed was wrong, I apologise for the hurt this has caused.

I hope you all continue to enjoy the discussion and I will read it with interest.

Humbly ....

Depends on your definition of "equality".

Typographically, they are not equal. In terms of data storage space, either persistent or volatile storage, they are not necessarily equivalent. Mathematically, they are equivalent. See, even "equal" has variations based on precision and linguistic ambivalence. But math is the language that claims to have absolute verbs, and "equals" is a verb, and mathematically, they are equal, by postulate.

You answered your own argument and disproved your own assertion. "... an infinitely recurring number..." is a set that doesn't include Pi.

You state a set that explicitly does not include a value, then use that value to disprove a quality of the set. It's like proving that apples aren't red by pointing at an orange.

If you want to prove that .9-repeats is not equal to 1, you need to post that proof in the language of mathematics, since that's the subject here. Essentially, you need to prove that 3/3rds isn't equal to 1. That's going to be rough.

You state that 0.3-repeats = 1/3 is an approximation, when it's actually not. It's a mathematically absolute equivalence. Anyone who knows how to do long division can prove it.

On the other hand, toung-in-cheek exercise is fun enough that I can't believe you're giving up on an impossible task so easily just to avoid straining your cheek! 😀

After a brief pause, almost had some coffee on the keyboard.

This was part of the discussion I had. That decimal representation isn't exact and that you can't represent some fractions acurately as decimals. Therefore you can't say .999... = 1 because it's not accurate to represent 1/9 or 1/3 as a decimal.

And I do find the philosophical discussion of the quantification of infinity quite intriguing. I think that a large part of this discussion is understanding that an infinitesimal is still a definite value (definitely infinite and there is a process for dealing with it in mathematics). People are stuck on what they think they know, what they've learned in school (even up through college) and are resistant to think outside the box.

arguments against have been-

x=.999...

-"you can't compare a complex number to a real number"

-".999 repeating will never equal 1, it's always .000...1 short"

1/3 = .333...

3 * .333... = .999...

3 * 1/3 = 1

-"1/3 cannot be represented accurately in decimal notation therefore you can't equate the two."

Only if you redefine portions of the language of math.

There are many fractions you can't represent accurately with decimals. Pi is the most famous. On the other hand, representing pi as a fraction fails the perfection test too.

But some fractions can be represented exactly with decimals, including any that either terminate at a finite point or become a finite group that repeats infinitely. 1/3 is one of the later (finite group = just the number 3, and it repeats infinitely). Some may not be practical to represent that way ("finite" can be pretty unweildy), but it is still possible to do so.

To say that 0.3-repeats isn't "precisely 1/3rd" is to redefine terminology within math, which means you're now operating in some other field of endeavor than math, and mathematical logic of course no longer applies.

Any discussion in which basic definitions (postulates) are subject to change without notice is, of course, pointless, except for entertainment purposes.

As an illustration of this, I once had someone assert to me that "evolution is impossible, nobody has ever seen one species change into another". This is untrue, especially in the field of microbiology, so I asked where he got that data. It turned out, he had redefined the word "species" to mean "having the same ancestors". By that definition, his statement was absolutely true. No child can have different ancestors than it's parent (except for the parents themselves, but that's a quibble). But that redefinition doesn't prove anything to anyone else, because it violates the agreement nature of language. Voltaire expressed this perfectly... but only if you accept his definitions of "argue", "define" and "terms". 🙂

This is perfectly valid if you're using a Pentium 90! :hehe: