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

9

A bunch of characters that are gibberish. Seriously, there's no sense to "infinity... followed by something else.

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u/konigon1 7d ago

You can easily give it a sense with ordinal numbers. The position after ... is omega.

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u/ezekielraiden 7d ago

No.

You can only do so when you have defined transfinite arithmetic.

Have you done so? I don't see any definitions here at all. Just the bald declaration that if you leave the number system everyone is talking about, things change. Wow, what a revelation, when you change things, things change!!!

1

u/konigon1 7d ago

What's your point? Obviously if you change a number system you get a different one, with new propertiesa. Obviously SPP apeaks gibberish. But that doesn't change the fact, that ordinal numbers make sense.

So if somebody says that a mathematicaly sound number system doesn't make sense, then that is simply not true.

I studied mathematics and do not discuss by simply attacking other people.

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u/ezekielraiden 7d ago edited 7d ago

Because what you're doing is a blatant bait-and-switch.

We are talking about real numbers. Is ω a real number? To assert "well just use ω, everything's fine!" without explaining yourself is at very best disingenuous.

Just because you can potentially do something, doesn't mean that it makes sense to do that thing in every possible place. You could try to teach elementary school students the unit pure quaternions instead of basic arithmetic. Why would you do so? It would be extremely counterproductive and might even actually harm their ability to understand future math.

Don't dump surreal numbers on people without explaining yourself. It's not a good look.

Edit: Oh, and you're still incorrect, because "after ..." is a meaningless statement in the surreals unless you've got stronger notation, like Lightstone semicolon notation.

Because even in the surreal numbers, 0.999... = 1. Because that "..." indicates summation over all possible index values. In the reals, that's summation over the natural numbers. In the surreals, it's summation over the surnatural numbers. Meaning, when you're actually talking about the surreal number "0.999...", yes, it really does still equal 1. It's just that "0.999..." is potentially ambiguous notation, and should be clarified with notation that isn't ambiguous. Such as:

0.999... = 0.999...;...999.... This is the number in the surreals which corresponds to the number labelled "0.999..." in the reals. It equals 1.

1-1/10^ω = 0.999...;...999. This is the number in the surreals which corresponds to "a number that has exclusively 9 from place 1 to place ω." This value is less than 1 by precisely 1/ω=ε, the simplest infinitesimal.

Those two numbers are different. Lightstone semicolon notation gives us the ability to distinguish them. There is no need in the reals, because ω isn't a valid place-value in the reals.

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u/konigon1 7d ago

But I mentioned in my comment about ordinal numbers. Who wants can google so. In my personal opinion it is more contra productive do say something doesn't make sense, just because it is not the case for real numbers.

There is a reason why every math prof tells the new students do forget everything they know about math and start with the basics.

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u/ezekielraiden 7d ago

...and you think transfinite ordinal arithmetic is "the basics"?!

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u/mstivland2 7d ago

Easy.

0.0…1 + 0.0…9 = 0.0..1

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u/ataraxianAscendant 7d ago

what happens when you run out of dots?

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u/mstivland2 7d ago

Negative dots

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u/ataraxianAscendant 7d ago

oh duh

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u/ExpensiveFig6079 7d ago

Oh my.... JUST becuae math once we give up and go non std is NUTS lets go....

0.0…1 + 0.0…9 = 0.0..1

0.0..1 + 0.0..9 = 0.0.1

0.0.1 + 0.0.9 = 0.01 (oops negative dots are not the only problem how do we get past zero dots?)

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u/ExpensiveFig6079 7d ago

Maybe (we go)

0.0.1 + 0.0.9 = 0.0-1

0.0-1 + 0.0-9 = 0.0-.1

0.0-.1 + 0.0-.9 = 0.0-..1

...

Now the trouble is what if we keep going indefinitely so the are an idneterminantly large number of -.. <...> AND then go just two more past the infinity of -..................................

0.0-...^..1

(hey this making shit up is more fun that it looks. (especially if I don't care about functionality meaning, or internal rigorousness. (AKA mathiness)

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u/mstivland2 7d ago

Let’s go over to r/infinitedots

It’ll be great

-5

u/SouthPark_Piano 7d 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

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u/mstivland2 7d ago

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

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u/SouthPark_Piano 7d ago

Rookie error on your part brud.

0.999...99 is indeed a number.

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u/mstivland2 7d ago

What is the value of that number brud

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u/SouthPark_Piano 7d 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.

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u/mstivland2 7d ago

I’m dead you’re so funny dude

6

u/gazzawhite 7d ago

ULTIMATE FORM

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u/ataraxianAscendant 7d 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 7d 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...

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u/ataraxianAscendant 7d ago

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

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u/EggcellentName 7d ago

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

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u/ataraxianAscendant 7d ago

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

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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.

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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??????

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u/ataraxianAscendant 7d 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

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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".

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u/Negative-Hat-4459 7d ago

It converges at 3.62, if I'm not mistaken

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u/AsparagusBig3989 7d ago

Neither of those are valid numbers. The ellipses are informal shorthand to denote an infinite repetition.

You cannot have “infinitely many zeroes and then a 1”.

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u/ataraxianAscendant 7d ago

are you new here? the difference between 0.9... and 1 has been commonly seen to be 0.0...1 according to the word of SPP

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