0.999... (infinity) = 1?

[-lexus-]

Alas, you got me.



But think of what you just said once again, 9 * 1/9 is actually mathematical manipulation.

In reality, how do you cut a piece of cake into 9 equal part?

Depends on the size of the cake though. If you have a rectangle shaped cake of 90 centimeters, you can cut it in 9 equal pieces no?

Besides, this trick only works in mathematics. I mean, like I quoted in the Wikipedia article, this works when you dont have to worry about the infinite decimals. If you do, then well, its technically not possible to get nine equal pieces of cake, but the difference between on piece and the other is a layer of atoms (or so small it cant be measured anymore). I think common sense then tells us not to complain about one layer of atoms more or less

 

[noex1337]

Its not ignoring a minute detail, its actually very logical. Lets use another one. 1/3 *3 = 1 right? 1/3 = 0.333... So 3* 0.333... = 1. That is the mathematical perspective.

Nevermind, I just noticed something. 1/3 != 0.3333333... That's just the closest we can get with the limitations of our number system. If you convert to base 3, the answer will be completely different. Now since that's annoying to do, I'll change the problem to something more manageable. We can all agree that 1/5 = 0.2 right? However, if you change that to binary, you get 0.0011001100110011001.....and if you multiply that by 5 (101 in binary) you get 0.11111111111111....... in binary (or something like that). As with our current problem, you could then argue that it's not equal to 1, but as you saw if you changed it back into decimal, that is not the case. All that goes to show is that different number systems have different numbers it doesn't like. That says nothing about the credibility or reality of mathematics.

Alas, you got me.



But think of what you just said once again, 9 * 1/9 is actually mathematical manipulation.

In reality, how do you cut a piece of cake into 9 equal part?

What exactly are you trying to ask here? Because it's entirely possible to distribute a cake into 9 pieces with equal mass, but is it ever necessary to be that precise?

 

[Undead-Cookie]

​

It is mathematically proven that 0.999... is equal to 1; however, mathematics isn't reality and neither reality is mathematics. Henceforth, speaking from the perspective of our common sense towards reality itself, can we justifiably say that 0.999... is equal to one? Equal or not equal, feel free to provide your argument,

First of all, a number somehow provides a limit, but infinity on the other hand cannot be 1 as it is cannot provide a limit.

How can it be infinite if it is 1?

And if I apply common sense, wouldn't infinity actually be 0?

A good example would be a droplet of water.

If it becomes infinite(actually it can't), it will disappear.(no?)

So it makes no sense to me when 0.999 becomes 1 in reality.

Though these are just my opinions.(Correct me if I am wrong).

Because it's entirely possible to distribute a cake into 9 pieces with equal mass, but is it ever necessary to be that precise?

But how can it be equal in size?(BTW, I didn't read the rest of the posts, just saw this one

).



Hint:

Let us try once again;





0,999... = 999.../1000...=1



999.../1000...=1



999...=1000...

Is that how they got 1?

But why are they dividing with each other?

And if 999... is = 1000 why even bother putting 1000?

I mean, couldn't they just divide like this :

999.../999... =

999... = 999..

Alas, you got me.

But think of what you just said once again, 9 * 1/9 is actually mathematical manipulation.

In reality, how do you cut a piece of cake into 9 equal part?

In infinity,the object is divided, when divided only 1 number is left.

But does this prove that it is 1 in reality? - A big no-no.

 

[FrantzS.]

​

It is mathematically proven that 0.999... is equal to 1; however, mathematics isn't reality and neither reality is mathematics. Henceforth, speaking from the perspective of our common sense towards reality itself, can we justifiably say that 0.999... is equal to one? Equal or not equal, feel free to provide your argument, and don't forget to also answer this next question; how valuable is common sense to Science?



PS: I emphasize this once again, I'm not asking for mathematical proof, I am asking for proof using our common sense.

Its not equal because they are not the same. There is a gap between the two numbers no matter how miniscule.

 

[Kaze Araki]

Thanks for checking my section. And pardon me for not able to address the more complex posts of yours in other threads due to time limitation, as it is currently 1AM midnight at my place. I have neither the strength nor the concentration to reply to the points you have raised - but I still hope to reply them tomorrow.

However, for this thread only, I can answer your remark by asking you a simple question;

Observe 1/3 and 0.333...; are they the same?
One seems to imply finite value, while the other of infinity.
But once again; are they the same, what do you think?

 

[Undead-Cookie]

I would still have to say no, because 0.999 is slightly below 1.

 

[Kaze Araki]

Well, it's not 0.999 - it's 0.999...
I think the real problem lies in how we write the division - for example; 22/7 - without ending up with a seemingly infinite value.
Something akin to optical illusion.

 

[Biomega]

think the real problem lies in how we write the division - for example; 22/7 - without ending up with a seemingly infinite value.

We did this in a maths class, but I don't know how exactly it is, or what topic it was for.

It went like this.

x^x^x^x^x... ad infinitum.

Then, y = 1 maybe infinity.(not sure)

∴ x = x^y or y^x or something like that.

Something like that. I don't know how it went. Of course, X is a variable of any positive integer.

(can we haz subscript and superscript bbcode, pl0x)

 

[noex1337]

Its not equal because they are not the same. There is a gap between the two numbers no matter how miniscule.

Check my previous most. That gap may not actually be there.

 

[Kamil]

The gap is infinitely small, so mathematically it doesn't exist. As for common sense, math was originally intended as a way to describe reality, and in reality cutting something into nine pieces doesn't change its mass or volume (assuming a perfect cut) even though 1/9 had to be given as 0.111... to be represented in the decimal system. From that 9/9=0.999... according to math. Common sense dictates that if you cut something into 9 pieces and take 9 of those pieces you have the whole thing so even if mathematics did not already have proof common sense would declare that 0.999... must equal 1.

And don't tell me there's too much math, 0.999... doesn't even exist outside of math so there's no other way to talk about it.