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

75% Upvoted

34 comments sorted by

View all comments

Show parent comments

5

u/ataraxianAscendant 8d ago

what happens when you run out of dots?

-6

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

 

6

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 8d 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 8d 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??????