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Anatoly

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Infinity

There are some types of infinity i'd like to discuss:

The first is the "last" ℕ number:
∞

The second type of infinity is the "first" ℤ number:
-∞

The last known type is ℚ, it is defined in geometry, on a segment [AB] where A represents 0, B represents 1, the next "dot" after A. We know that the dot is infinite.
1/∞ ~ 0

My question is simple: Have you ever used in any operations infinity? If you have, may you show me how to work with it? The next question would be: Which other types of infinity have you discovered?

Just fun question.

LukeM

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Re: Infinity

The last known type is ℚ, it is defined in geometry, on a segment [AB] where A represents 0, B represents 1, the next "dot" after A. We know that the dot is infinite.

I dont get what you mean by this one (tried googling it and couldnt find anything)

Ive used positive and negative infinity though

Anatoly

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Re: Infinity

The last known type is ℚ, it is defined in geometry, on a segment [AB] where A represents 0, B represents 1, the next "dot" after A. We know that the dot is infinite.

I dont get what you mean by this one (tried googling it and couldnt find anything)

Ive used positive and negative infinity though

The last is 0.0000000000000000000000000 .... infinite zeros' ....0000000000001

LukeM

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From: England

Joined: 2016-06-03

Posts: 3,009

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Re: Infinity

▼LukeM wrote:

▼AnatolyEE wrote:

The last known type is ℚ, it is defined in geometry, on a segment [AB] where A represents 0, B represents 1, the next "dot" after A. We know that the dot is infinite.

I dont get what you mean by this one (tried googling it and couldnt find anything)

Ive used positive and negative infinity though

The last is 0.0000000000000000000000000 .... infinite zeros' ....0000000000001

Oh ok , I wouldnt call it infinity, but yes, I get what you mean now
Ive probably used it before but would just assume its equal to 0, the same as 9.9999... = 10

TundrumMax

Formerly Memomemo

Joined: 2017-10-26

Posts: 447

Re: Infinity

▼LukeM wrote:

▼AnatolyEE wrote:

The last known type is ℚ, it is defined in geometry, on a segment [AB] where A represents 0, B represents 1, the next "dot" after A. We know that the dot is infinite.

I dont get what you mean by this one (tried googling it and couldnt find anything)

Ive used positive and negative infinity though

The last is 0.0000000000000000000000000 .... infinite zeros' ....0000000000001

Oh ok , I wouldnt call it infinity, but yes, I get what you mean now
Ive probably used it before but would just assume its equal to 0, the same as 9.9999... = 10

ok, what about 5.555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555

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LukeM

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From: England

Joined: 2016-06-03

Posts: 3,009

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Re: Infinity

▼LukeM wrote:

▼AnatolyEE wrote:

▼LukeM wrote:

▼AnatolyEE wrote:

The last known type is ℚ, it is defined in geometry, on a segment [AB] where A represents 0, B represents 1, the next "dot" after A. We know that the dot is infinite.

I dont get what you mean by this one (tried googling it and couldnt find anything)

Ive used positive and negative infinity though

The last is 0.0000000000000000000000000 .... infinite zeros' ....0000000000001

Oh ok , I wouldnt call it infinity, but yes, I get what you mean now
Ive probably used it before but would just assume its equal to 0, the same as 9.9999... = 10

ok, what about 5.5555555555555555555555(...)

50/9 Or five point five recurring

Anatoly

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Re: Infinity

Ive used positive and negative infinity though

Can I get examples?

▼LukeM

▼LukeM wrote:

▼AnatolyEE wrote:

The last known type is ℚ, it is defined in geometry, on a segment [AB] where A represents 0, B represents 1, the next "dot" after A. We know that the dot is infinite.

I dont get what you mean by this one (tried googling it and couldnt find anything)

Ive used positive and negative infinity though

The last is 0.0000000000000000000000000 .... infinite zeros' ....0000000000001

Oh ok , I wouldnt call it infinity, but yes, I get what you mean now
Ive probably used it before but would just assume its equal to 0, the same as 9.9999... = 10

ok, what about 5.555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555

It's a rational number.

Infinity isn't belonging to the definition of rational numbers (Definition: = / )

▼LukeM wrote:

▼AnatolyEE wrote:

The last known type is ℚ, it is defined in geometry, on a segment [AB] where A represents 0, B represents 1, the next "dot" after A. We know that the dot is infinite.

I dont get what you mean by this one (tried googling it and couldnt find anything)

Ive used positive and negative infinity though

The last is 0.0000000000000000000000000 .... infinite zeros' ....0000000000001

Oh ok , I wouldnt call it infinity, but yes, I get what you mean now
Ive probably used it before but would just assume its equal to 0, the same as 9.9999... = 10

Or 9.(9) = 10 - 1/∞ ~ 10

Zumza

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From: root

Joined: 2015-02-17

Posts: 4,645

Re: Infinity

You'll soon study limits, probably. There you'll use this the most

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kreacher

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From: Wakanda

Joined: 2015-03-31

Posts: 409

Re: Infinity

Or 9.(9) = 10 - 1/∞ ~ 10

Oh cool thats how you write it. I just thought that 10=9.9 recurring but I see what you mean now. We never learn anything interesting in our classes like that even though we are in set 1 yr 10.

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Anatoly

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Re: Infinity

Or 9.(9) = 10 - 1/∞ ~ 10

Oh cool thats how you write it. I just thought that 10=9.9 recurring but I see what you mean now. We never learn anything interesting in our classes like that even though we are in set 1 yr 10.

We aren’t learning anythin* interesting in our German school either. This is from Russian school, and I taught myself infinity.

kreacher

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From: Wakanda

Joined: 2015-03-31

Posts: 409

Re: Infinity

lol I'm doing linear equations for like the infinitieth time lol and its so ez it actually hurts my brain

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Est. December 2010

LukeM

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From: England

Joined: 2016-06-03

Posts: 3,009

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Re: Infinity

Or 9.(9) = 10 - 1/∞ ~ 10

Oh cool thats how you write it. I just thought that 10=9.9 recurring but I see what you mean now. We never learn anything interesting in our classes like that even though we are in set 1 yr 10.

Well there is an actual proof that they are equal:

    10x = 9.9999...
      x = 0.9999...
10x - x = 9
     9x = 9
      x = 1 (10x = 10)

kreacher

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From: Wakanda

Joined: 2015-03-31

Posts: 409

Re: Infinity

crap i forgot about that oh well they both kinda work

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HeyNK

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Joined: 2017-04-07

Posts: 1,318

Re: Infinity

countable infinities VS uncountable infinities

Anatoly

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Re: Infinity

▼kreacher wrote:

Or 9.(9) = 10 - 1/∞ ~ 10

Oh cool thats how you write it. I just thought that 10=9.9 recurring but I see what you mean now. We never learn anything interesting in our classes like that even though we are in set 1 yr 10.

Well there is an actual proof that they are equal:

    10x = 9.9999...
      x = 0.9999...
10x - x = 9
     9x = 9
      x = 1 (10x = 10)

The proof makes sense, but if you think geometrical. You got a segment, and you take the “next” point from the end, that this point won’t be the same...

Btw.
Is 1/∞ a real number?

HeyNK

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Joined: 2017-04-07

Posts: 1,318

Re: Infinity

Well this is what it is:

   lim        1
              ----   =   0
x -> ∞     x

Which is actually very similar to how it works in EE, as you will recall:

   lim           
                  ----   =   
->      

Anatoly

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Re: Infinity

A beautiful representation of infinity. For a reason I thought I already posted this.

Pingohits

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From: aids lizard

Joined: 2015-02-15

Posts: 7,591

Re: Infinity

although the screen gets smaller and smaller due to visual feedback, it DOES reach a point where it can no longer be visible. In this case, the smallest "increment" the image can reach is a single pixel, which limits the recursion and renders your analogy of "infinity" null.

a better example would be an infinity mirror

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LukeM

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From: England

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Posts: 3,009

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Re: Infinity

a better example would be an infinity mirror

But surely light would also have a fundamental minimum perceivable area (albeit tiny compared to a pixel) due to random slight changes in the beam or diffraction through the glass / air, and failing that probably the planck length

Pingohits

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From: aids lizard

Joined: 2015-02-15

Posts: 7,591

Re: Infinity

a better example would be an infinity mirror

But surely light would also have a fundamental minimum perceivable area (albeit tiny compared to a pixel) due to random slight changes in the beam or diffraction through the glass / air, and failing that probably the planck length

That is precisely correct, but notice I am not stating an infinity mirror is perfectly infinite. I am merely stating an infinity mirror is a better example than screen recursion. The Planck length is a human construct and can be disregarded, even though any measure beyond that is completely useless. Same reason with that argument of an "instant". An instant is an infinitely small timeframe that cannot possibly be comprehended nor measured, but it is still something that "exists". In fact, I believe the definition of a theoretical "instant" to be an even better representation of infinite, albeit in a different form (infinite in terms of time, not space, as well as tending to zero instead of, well, infinity)

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Ratburntro44

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Re: Infinity

There are some types of infinity i'd like to discuss:

The first is the "last" ℕ number:
∞

The second type of infinity is the "first" ℤ number:
-∞

not strictly but ∞ and -∞ can be reasonably used in a number of contexts

The last known type is ℚ, it is defined in geometry, on a segment [AB] where A represents 0, B represents 1, the next "dot" after A. We know that the dot is infinite.
1/∞ ~ 0

i've never heard of anyone using ℚ to mean an infinitesimal
moreover, even with infinitesimals, "next" isn't something that really has a meaning on the rational (at least in a sense corresponding to <) or real numbers

The last is 0.0000000000000000000000000 .... infinite zeros' ....0000000000001

not how decimals work (at least in any standard usage)

Infinity isn't belonging to the definition of rational numbers (Definition: = / )

not really how the rationals are defined but i guess it makes sense in a certain very casual way

Or 9.(9) = 10 - 1/∞ ~ 10

Oh cool thats how you write it. I just thought that 10=9.9 recurring but I see what you mean now. We never learn anything interesting in our classes like that even though we are in set 1 yr 10.

please don't take his word as fact

Well there is an actual proof that they are equal:

    10x = 9.9999...
      x = 0.9999...
10x - x = 9
     9x = 9
      x = 1 (10x = 10)

this isn't really that much of a proof but it is a nice demonstration of why you might want to work in a system where they are equal (as people do)

countable infinities VS uncountable infinities

something that actually exists though to be pedantic there's only one countably infinite cardinal

The proof makes sense, but if you think geometrical. You got a segment, and you take the “next” point from the end, that this point won’t be the same...

yes but (not entirely formally speaking) the length of that point is 0

Is 1/∞ a real number?

no

although the screen gets smaller and smaller due to visual feedback, it DOES reach a point where it can no longer be visible. In this case, the smallest "increment" the image can reach is a single pixel, which limits the recursion and renders your analogy of "infinity" null.

this is a pretty pointless thing to point out

LukeM

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From: England

Joined: 2016-06-03

Posts: 3,009

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Re: Infinity

Well there is an actual proof that they are equal:

    10x = 9.9999...
      x = 0.9999...
10x - x = 9
     9x = 9
      x = 1 (10x = 10)

this isn't really that much of a proof but it is a nice demonstration of why you might want to work in a system where they are equal (as people do)

I wouldn't say it's a particularly formal proof, but I would still call it a proof (if not then where's the assumption or error?)

Edit: Also infinitesimal numbers are a thing and they =/= 0 (by definition), I think AnatolyEEs problem was that there isn't a very good numerical representation (don't think you can write them as 0.00...001) although I think his point explanation would be correct

peace

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Re: Infinity

also take the number PI it has so much decimals

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thanks hg for making this much better and ty for my avatar aswell

Bimps

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Posts: 5,067

Re: Infinity

also take the number PI it has so much decimals

how many

peace

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Posts: 9,226

Re: Infinity

also take the number PI it has so much decimals

how many

idfk lol prob infinite but how did people know

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thanks hg for making this much better and ty for my avatar aswell