Is it true that 1 = 0.999…? And Exactly Why or Why Not?

Yes, 1 = 0.999…

No, 1 ≠ 0.999…

Other

0voters

This is one of those issues that display the clear distinction between a good philosopher and a expert mathematician. The good philosopher will tell that they cannot be equal and the modern day mathematician will tell you that they are declared to be equal by mathematicians.

Currently Wiki, and a great many mathematicians will tell you that 1 = 0.999… Many “proofs” are displayed to show how wrong those are who disagree. The “good philosopher” can display how every one of those proofs are fallacious.

What is your belief?

And WHY?

Note that you can change your poll-vote later if you wish.

No one is going to support Wiki and the mathematicians???

When I came here years ago, anything said by Wiki, mathematicians, and certainly physicists (if there is any longer a difference), was holy doctrine. And now you cast stones???

I do not think that they are the same for they occupy different places on the number
line but they are however as close to each other as any two numbers can possibly be

I cannot fault them. But now that I think about it it is wrong to place an irrational number on a specific place on the number line because if it has
an infinite number of decimal places then one cannot be absolutely certain where it goes. One can only be probably certain. Incidentally whoever
told you that mathematicians and physicists are perfect is wrong because this is not a quality human beings possess at all. And while mathematics
[ but not physics as it is a science and therefore inductive ] may be a perfect discipline those who practice it are just as fallible as everybody else

To have either 0.9r or 1, you have to have something exact as the standard. As there are no exact standards [improbability etc] then neither case is exactly true to begin with.

The maths has to rely on a metaphoric pretext where numbers aren’t real and present their own logic standards. math is of course metaphor, but unless it marries to what reality is then its conclusions are irrelevant. as that’s impossible then maths/science will just have to remain as part of philosophy.

basically there is a degree of ambiguity in any case.

reality does not divide perfectly, not in shape/geometry nor numbers/patterns imho.

I thought it was because it has infinite decimal places. However that alone does not make it irrational
according to Wikipedia because it has to be random or non repeatable too such as with pi for example

Even if it was not equal to one according to that proof it would still be a rational number since it is not random or non repeatable. Even though
it has an infinite number of decimal places the same as any irrational number. Any number whether rational or irrational can be expressed as a
fraction but only rational ones technically count as fractions. Because neither the numerator or denominator can tend to infinity. Interestingly
though most numbers are actually irrational as Wikipedia correctly says

I have to correct myself when I said I did not think 0.999 … is equal to I because they are the same number just expressed differently
The Wiki proof is correct and is accepted by mathematicians. It does appear counter intuitive but that does not actually make it false

The question demonstrates a quirk of human perception and the limitations of the decimal system. It’s similar to an optical illusion but it’s a mental illusion.