This makes sense: 0.99 = 1

scratchisthebest

My favorite way:

If you put something over an equal amount of 9s, it's a repeating decimal of that number.

1234
----    0.1234123412341234...
9999

45
--      0.4545454545454545...
99

Let's try it with 9/9:

9
-       0.9999999999999999...
9

But wait, anything put over itself is always 1, and 9/9 = 1.
Therefore 0.999... has to equal 1 as well.

Last edited by scratchisthebest (June 23, 2016 02:29:56)

Jonathan50

Firedrake969 wrote:

Jonathan50 wrote:

jokebookservice1 wrote:

0.99999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999 (there will be a 1 at the end, just give me an uncountably (iirc) infinite amount of years to finish this and put an 8

You mean 0.999…1 (is that how you write it)? That's less than 0.999….

Unless there's an infinite amount of 9s - then it's meaningless to say “at the end of infinity”

That does not have it more than 0.999…! (And of course there is an infinite amount of 9s!)

Last edited by Jonathan50 (June 23, 2016 02:44:59)

Jonathan50

Jonathan50 wrote:
0.99 is not 1… “0.999…” and “0.99” are different.

Firedrake969

Jonathan50 wrote:
Firedrake969 wrote:
Jonathan50 wrote:
jokebookservice1 wrote:
0.99999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999 (there will be a 1 at the end, just give me an uncountably (iirc) infinite amount of years to finish this and put an 8
You mean 0.999…1 (is that how you write it)? That's less than 0.999….
Unless there's an infinite amount of 9s - then it's meaningless to say “at the end of infinity”
That does not have it more than 0.999…! (And of course there is an infinite amount of 9s!)

exactly

Jonathan50 wrote:
Jonathan50 wrote:
0.99 is not 1… “0.999…” and “0.99” are different.

semantics - OP probably forgot the ellipses.

Jonathan50

Firedrake969 wrote:
Jonathan50 wrote:
Firedrake969 wrote:
Jonathan50 wrote:
jokebookservice1 wrote:
0.99999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999 (there will be a 1 at the end, just give me an uncountably (iirc) infinite amount of years to finish this and put an 8
You mean 0.999…1 (is that how you write it)? That's less than 0.999….
Unless there's an infinite amount of 9s - then it's meaningless to say “at the end of infinity”
That does not have it more than 0.999…! (And of course there is an infinite amount of 9s!)
exactly

? I said "That's less“, then you said ”Unless there's an infinite amount of 9s“ (which of course there are!), so I replied ”That does not have it more“ (I meant make it more but whatever) and you say ”exactly"??

Last edited by Jonathan50 (June 23, 2016 02:50:39)

Firedrake969

Jonathan50 wrote:
Firedrake969 wrote:
Jonathan50 wrote:
Firedrake969 wrote:
Jonathan50 wrote:
jokebookservice1 wrote:
0.99999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999 (there will be a 1 at the end, just give me an uncountably (iirc) infinite amount of years to finish this and put an 8
You mean 0.999…1 (is that how you write it)? That's less than 0.999….
Unless there's an infinite amount of 9s - then it's meaningless to say “at the end of infinity”
That does not have it more than 0.999…! (And of course there is an infinite amount of 9s!)
exactly
? I said "That's less“, then you said ”Unless there's an infinite amount of 9s“ (which of course there are!), so I replied ”That does not have it more“ (I meant make it more but whatever) and you say ”exactly"??

1. jokebookservice1 implied an infinite number of 9s
2. You said it's less
3. I said that it's not less, assuming that there is an infinitely long chain of 9s after the decimal
4. I never said that it was more - I said it wasn't less. If something's not more or not less, that generally means it's equal.
5. You got confused
6. I tried to explain
7. You'll either understand or reply with some amount of question marks, possibly with words as well
9. I like writing lists like this
10. You're probably questioning why I'm writing so much other random stuff
11. I skipped #8
12. You looked back for it
13. Confusion still ensues

Ethan_1

joefarebrother wrote:
My favourite way of intuitively explaining it is, if 0.9999… was different from 1, there would be a number between the two. Can you write down such a number? No.

I have never heard this one before. I guess I don't entirely see the argument that because there is no number between them, they are equal. If we restrict ourselves to integers (-2, -1, 0, 1, 2, 3, etc), there is no integer between 2 and 3 (which I hope we can all agree are not equal). So I guess I don't really see your argument holding up….

Perhaps my logic is confounded by the fact that integers are discrete, and real numbers are not?

Last edited by Ethan_1 (June 23, 2016 07:25:22)

IcyCoder

Proof that it equals 1 using algebra (source):

x=0.999
10x=9.999

10x=9.999
1x=0.999
————-
9x=9.000

9/9=1

What do u guys think?

Firedrake969

Ninja'd https://scratch.mit.edu/discuss/topic/205215/?page=1#post-2059936

IcyCoder

Firedrake969 wrote:
Ninja'd https://scratch.mit.edu/discuss/topic/205215/?page=1#post-2059936

Boo though mine is more simplistic

Lythium

Ethan_1 wrote:
joefarebrother wrote:
My favourite way of intuitively explaining it is, if 0.9999… was different from 1, there would be a number between the two. Can you write down such a number? No.
I have never heard this one before. I guess I don't entirely see the argument that because there is no number between them, they are equal. If we restrict ourselves to integers (-2, -1, 0, 1, 2, 3, etc), there is no integer between 2 and 3 (which I hope we can all agree are not equal). So I guess I don't really see your argument holding up….

Perhaps my logic is confounded by the fact that integers are discrete, and real numbers are not?

But there are numbers between 2 and 3. The problem with your argument is that you're restricting yourself to integers, while Joe's clearly not.

Ethan_1

Lythium wrote:
Ethan_1 wrote:
joefarebrother wrote:
My favourite way of intuitively explaining it is, if 0.9999… was different from 1, there would be a number between the two. Can you write down such a number? No.
I have never heard this one before. I guess I don't entirely see the argument that because there is no number between them, they are equal. If we restrict ourselves to integers (-2, -1, 0, 1, 2, 3, etc), there is no integer between 2 and 3 (which I hope we can all agree are not equal). So I guess I don't really see your argument holding up….

Perhaps my logic is confounded by the fact that integers are discrete, and real numbers are not?
But there are numbers between 2 and 3. The problem with your argument is that you're restricting yourself to integers, while Joe's clearly not.

Yes, I know that is the difference. But then would you say that two consecutive numbers are equal? That seems to be joefarebrother's logic….

But that doesn't intuitively make sense to me.

Ethan_1

scratchisthebest wrote:

My favorite way:

If you put something over an equal amount of 9s, it's a repeating decimal of that number.

1234
----    0.1234123412341234...
9999

45
--      0.4545454545454545...
99

Let's try it with 9/9:

9
-       0.9999999999999999...
9

But wait, anything put over itself is always 1, and 9/9 = 1.
Therefore 0.999... has to equal 1 as well.

Wow. O.O that is elegant. Def using this from now on.

MegaApuTurkUltra

Ethan_1 wrote:

scratchisthebest wrote:

My favorite way:

If you put something over an equal amount of 9s, it's a repeating decimal of that number.

1234
----    0.1234123412341234...
9999

45
--      0.4545454545454545...
99

Let's try it with 9/9:

9
-       0.9999999999999999...
9

But wait, anything put over itself is always 1, and 9/9 = 1.
Therefore 0.999... has to equal 1 as well.

Wow. O.O that is elegant. Def using this from now on.

But that's not a full proof. The reason the decimals always look like that is because of the geometric series for the thing. You have to mention that

BookOwl

scratchisthebest wrote:
My favorite way:
If you put something over an equal amount of 9s, it's a repeating decimal of that number.

How do you know that for sure?

MegaApuTurkUltra

BookOwl wrote:
scratchisthebest wrote:
My favorite way:
If you put something over an equal amount of 9s, it's a repeating decimal of that number.
How do you know that for sure?

Well x/y where y is some number of nines is the same as x/(1 - 1/(y+1)) so we have a geometric series with a1 = x and r=1/(y+1) which is the next multiple of 10 after y. Thus x repeats in the decimal

Last edited by MegaApuTurkUltra (June 23, 2016 16:01:58)

jokebookservice1

Ethan_1 wrote:
Lythium wrote:
Ethan_1 wrote:
joefarebrother wrote:
My favourite way of intuitively explaining it is, if 0.9999… was different from 1, there would be a number between the two. Can you write down such a number? No.
I have never heard this one before. I guess I don't entirely see the argument that because there is no number between them, they are equal. If we restrict ourselves to integers (-2, -1, 0, 1, 2, 3, etc), there is no integer between 2 and 3 (which I hope we can all agree are not equal). So I guess I don't really see your argument holding up….

Perhaps my logic is confounded by the fact that integers are discrete, and real numbers are not?
But there are numbers between 2 and 3. The problem with your argument is that you're restricting yourself to integers, while Joe's clearly not.
Yes, I know that is the difference. But then would you say that two consecutive numbers are equal? That seems to be joefarebrother's logic….

But that doesn't intuitively make sense to me.

With integers, you are correct.

However, if you don't restrict yourself to integers then you can say that

y = y / 2

if you repeat this an arbitrary number of times, with y initialized to 1, you will keep closing in on numbers closer and closer to 0 without reaching it. So now they are equal. There are numbers between 2 and 3, 2.5, you cannot restrict yourself to integers here

flutehamster

nvm

Last edited by flutehamster (June 23, 2016 17:42:23)

joefarebrother

Ethan_1 wrote:
joefarebrother wrote:
My favourite way of intuitively explaining it is, if 0.9999… was different from 1, there would be a number between the two. Can you write down such a number? No.
I have never heard this one before. I guess I don't entirely see the argument that because there is no number between them, they are equal. If we restrict ourselves to integers (-2, -1, 0, 1, 2, 3, etc), there is no integer between 2 and 3 (which I hope we can all agree are not equal). So I guess I don't really see your argument holding up….

Perhaps my logic is confounded by the fact that integers are discrete, and real numbers are not?

The real numbers and the rational numbers are dense, which means ALL distinct numbers in those fields have a number between them. The integers are NOT dense, which is why that argument does not extend to integers.

BKFighter

Guys, lets disprove this the programmer way.

var x = 0.999999999999999999999999999999 //Close enough
var y = 1
if(x===y){
console.log("Equal");
}else{
console.log("Not Equal");
}

WHAT JUST HAPPENED!!!!!!!!! I PUT THAT IN THE CONSOLE AND IT SAID THEY WERE EQUAL!!!!!!!!!!!!!!!!!!!! AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHH!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!

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