1 = .9999.....

[Aydin]

............ I failed Algebra II..

You guys are really smart... >_<

[Madame Adequate]

And no amount of evidence or reasoning will make me see that the infinitely small difference between 0.999... and 1 does not exist

"Evidence and proof will not convince me!"

[blackmage_nuke]

Yes Im like a hardcore christian except in a non religous way

[Peegee]

It's okay man. I'll just be relentlessly logical until you grudgingly accept.

It's how I was taught.

Take a really small real number. Say one divided by the amount of prions in the universe. In practical reality something that small does not exist, but in mathematics it does.

Now with that number you divide it by two. Oh crap you have an even smaller real number! Divide it again! and again! Divide it by the inverse of itself! Oh crap it became even more smaller! Do it again and again!

You can do this "infinitely" and it would always be a smaller real number. There is no such thing as a smallest real number greater than zero.

Once I realized that, 0.999... ceased to be an irrational number

[blackmage_nuke]

Programing has lead me to believe that whoever wrote the universe has included some version of

#include<limits>
#define fltmin numeric_limits<float>::min()

for the universe. Except rather than float we use all numbers

[Peegee]

Programing has lead me to believe that whoever wrote the universe has included a

#include<limits>
#define fltmin numeric_limits<float>::min()

for the universe

English.

[blackmage_nuke]

Well in programming there is a smallest number greater than 0 and I believe the universe is a giant program. When I learnt about Planck lengths that blew my mind

[blackmage_nuke]

Yes mathematics commonly has sexual intercourse with other sciences. No matter how many large english's breasts get, maths just doesnt swing that way

[Quindiana Jones]

Decimals and fractions are different. 1 does not equal 0.999.....

[qwertysaur]

In Math to prove something fully, you also have to disprove it is false. You can not disprove that 0.999999... =/= 1, therefore the statement is not true. (when you disprove falsehood you use indirect proofs usually)

Infinity can never be reached, only approached, and also does not actually exist in math. The full proven statement here is that as the number of digits after the decimal place approaches infinity, the value of the number (which is still rational) approaches 1, but never quite reaches it.

[Raistlin]

Let ".999..." equal a decimal followed by an infinite series of nines.

Ok, all of you who are claiming that .999... does not equal one are wrong. The number between them is not "infinitely small," because there is no number between them. They are not "basically equal with rounding," they are in fact exactly equal.

Three thirds together make a whole, so the number .999... is a human construct that doesn't exist in the practical world.

Yeah it does. I'm pretty sure you can identify a single object in the "practical world". ".999..." is just a different representation of it, but just as valid as "1."

It's from this misunderstanding that the equation 1/3 + 2/3 = 3/3 / 0.333... + 0.666... = 0.999.... can arise, because you're essentially adding together decimals that aren't a correct representation of the fraction being shown. You can't add infinite series of decimals together even if logically they make sense because they are infinitely long.

This makes no sense. It's not a "misunderstanding," it's adding together rational numbers.

This is a falsity because it only applies to finite decimal values. If a given value is an infinite series then it becomes impossible to locate it within a number line because of this as the inherent value of that number is impossible to place.

This is also wrong, and I'm not even sure where you got this. It is a basic rule of algebra that any two, distinct real numbers have an infinite number of other distinct, real numbers between them. 0.999... is a real number.

Someone who remembers more calculus than me will have to post the actual proof. It was posted a couple of years ago in the last thread but I'm too lazy to look it up. But yes, it is actually, definitively proven that .999... = 1.

EDIT: Ok, previous threads on this: First one. Second one. Third one.

[Rantz]

Three thirds together make a whole, so the number .999... is a human construct that doesn't exist in the practical world.

Yeah it does. I'm pretty sure you can identify a single object in the "practical world". ".999..." is just a different representation of it, but just as valid as "1."

I'm not talking about what the rules about mathematics are, I'm debating the actual merit of ever using the representation .999... when all it does is cause confusion. Some would undoubtedly say that the .999... representation exists to increase clarity, but as proven by this discussion and countless others, it clearly does just the opposite. The simple fact that they are equal renders the representation .999... obsolete as far as I'm concerned.

[Denmark]

Well in programming there is a smallest number greater than 0 and I believe the universe is a giant program.

Programming is not mathematics. Programming is defined, restricted, by the limits of the computer. Computers cannot comprehend infinity. Most humans can't comprehend infinity, why should a commercially-available machine MADE BY HUMANS be able to do it? When you see "infinity" on a computer, that's just a pre-defined bitstring that the computer interprets as "infinity", just like all other numbers are pre-defined bitstrings interpreted as the computer as explicit numbers. If you desire, I would be glad to have a sitdown discussion with you about computer architecture.

The universe, on the other hand, is not limited. This is the reason why we have the <b>concept</b> (did you get that) of infinity, because the human mind can comprehend this concept and it is a useful concept in mathematics.

Your "belief" that the universe is a giant program does not make it so. Reject your beliefs and accept science.

tl;dr - stop trollin and lrn2math

[blackmage_nuke]

The universe has it's limits, or atleast you cant prove it doesnt

[Vyk]

If you use it in something its going to come out so close it won't really matter. But technically and logically they are different

If you placed the lines on a graph, they'd be close. You might argue they'd even be touching. But they wouldn't be the exact same