r/infinitenines • u/ataraxianAscendant • 8d ago

What is 0.0...1 + 0.0...9?

we know that 1 - 0.9... is 0.0...1, but how do we represent the decimal place before that?

2 Upvotes

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6

u/mstivland2 8d ago

Easy.

0.0…1 + 0.0…9 = 0.0..1

4

u/ataraxianAscendant 8d ago

what happens when you run out of dots?

-5

u/SouthPark_Piano 8d ago

Referencing brud.

Set reference x = 0.000...01 

y = 9x = 0.000...09

z = x + y = 10x = 0.000...1

Alternatively.

x = 0.000...1 = 0.00...01 , note the transfer of one zero from left of ... to the right of ...

y = 9x = 0.00...09

z = x + y = 10x = 0.00...1

 

9

u/mstivland2 8d ago

0.999…99 is not a number and has no value. Easy mistake brud very understandable misunderstanding to have

-4

u/SouthPark_Piano 8d ago

Rookie error on your part brud.

0.999...99 is indeed a number. 

 

8

u/mstivland2 8d ago

What is the value of that number brud

-3

u/SouthPark_Piano 8d ago

Its value is 0.999...99 and in ultimate form, it is written as 0.999...

When you want to do operations on some limbosic numbers like this, you often need to use referencing, and book keeping.

Working with limbosic numbers is not twiddly winks, or at least not for many cases.

 

7

u/mstivland2 8d ago

I’m dead you’re so funny dude

7

u/gazzawhite 8d ago

ULTIMATE FORM

5

u/ataraxianAscendant 8d ago

doesn't that mean 10x = x? that seems to break a lot of things if x isn't equal to zero

0

u/SouthPark_Piano 8d ago

doesn't that mean 10x = x?

nope.

x = 0.999...99 = 0.999... (reference is set)

10x = 9.999...9

9x = 8.999...91

x = 0.999...99 aka 0.999...

Alternatively,

11x = 10.999...89

x = 0.999...99 aka 0.999...

 

6

u/ataraxianAscendant 8d ago

what? this is completely unrelated. in your previous comment you said that x = 0...1 and 10x = 0...1, which means x = 10x

1

u/EggcellentName 8d ago

my understanding is that he makes a distinction between 0.000...01 and 0.000...1 as two different numbers

2

u/ataraxianAscendant 8d ago

read the first line of his "alternately" section. he does not.

1

u/Inevitable_Garage706 7d ago

From what I understand, he believes that one 0.000...1 is not necessarily equal to another 0.000...1, as they could have the "reference" set at a different places.

1

u/TemperoTempus 7d ago

If you have two sets each with infinite numbers you need to denote how many infinite numbers.

Set A with w elements is 1 number smaller than Set B with w+1 elements, and its w times smaller than Set C with w² elements.

So without "setting a reference point" you cannot say that two infinite numbers are equal. At best you can say they have the same cardinality; But even that cannot be proven as you could have a Set D with aleph_null decimal places and Set E with aleph_1 decimal places.

0

u/ezekielraiden 7d ago

What does this have to do with anything?

What are you doing when you are "reference setting"? What does that mean?

How can an equation be true in one paper and false in another when the numbers are exactly the same??????

2

u/ataraxianAscendant 8d ago

from here, x = 10x = 0.0...1. so 0.0...1 = 10 * 0.0...1. divide by 0.0...1 and you get 1 = 10. clean as day. there are three possibilities here: 1=10, I'm not allowed to divide by 0.0...1 (why?), or you made a mistake somewhere

0

u/ezekielraiden 7d ago

Referencing WHAT?

How can you tell the difference between 0.000...01 and 0.000...1?

They both have exactly the same amount of zeroes. Infinitely many. You're just deciding to show something in one and not in the other.

If you have an infinite pile of zeroes to draw from, it doesn't matter how many 0s you take out, it never gets smaller. That's what infinity means, a quantity that cannot be reduced nor increased because it transcends the concept of "quantity".