Is 1 = 0.999... ? Really?

1 cannot equal 0.999…
1 = 1 and 0.999… = 0.999…

Compare the following:

  1. That room is 9m long
  2. That room is 9.999…m long
  3. That room is 999…m long
  4. That room is 999…cm long
  5. That room is infinitely long

9m encompasses the measure 8.999…m and everything less than it. 9.999…m is a measure just as 8.999…m is a measure. 3 and 4 are identical in size because once infinity enters the equation, it makes no difference if the measuring unit is m or cm. 3, 4, and 5, amount to the same thing, though expressed differently. If we say 6) that room is 222…m long or 7) 111…km long, again we are saying 5 just with different symbols that would be relevant or significant in a finite context. Not in this context.

That there is one Existence, cannot be denied. That It is Infinite cannot be denied. That It accommodates (makes hypothetically possible) things within it that can have a beginning but no end, cannot be denied. Call such endless things with beginnings x. Call Existence E. Clearly, E and x are different. All xs are encompassed/sustained/made possible by E. As in the set of all xs is E. There’s only one E, but there can be an endless number of xs. xs cannot be independent of E. E cannot be independent of E, therefore, E is truly independent/self-sufficient and self-containing/encompassing. E is truly/completely Infinite. No other thing is truly/completely Infinite. No other thing is complete Infinity.

CR:

In strange loops: x is e.

Look up this concept. It’s very well known.

Also:

Look up holograms, also very well known.

I think it’s interesting to note the following:

9.999… is bigger than 8.999… but 8.999… is the same size as 8.111…

It’s as if the Infinitesimal/Infinite is what connects/separates 8 to/from 9 with 8.111… and 8.999… and all other 8.123… highlighting that connection.

Is this not more reason to think that Existence is in us and we are in It?

You’re talking about a lot of different things here that you didn’t clarify.

Is the number 1 infinite?

Well… you think it’s greater than all infinitesimals combined.

Well…What then about the number 2?

It’s twice as great as all infinitesimals combined.

But if we’re talking about infinity, it’s a concept of endless, which means that infinitesimals are greater than 1… all of them!

But you say 1 is the greatest (the supreme)

Let me put it this way…

If you added all the infinitesimals together, they’d all add up to less than infinity… that’s a contradiction because they ARE infinite!

No

I don’t

It’s a finite number like the number 1, 5, or 48934892480

There is no ‘all infinitesimals’. There is the Infinite and the Infinitesimal. They are both One and the Same. There is only One of It.

1 is finite, so is 2, so is every other finite number. This is distinct from that which is truly Infinite (E), which both sustains/encompasses and separates all xs and finites from each other.

Just cherry pick me, fine.

I’ll reiterate…

If you add all the infinitesimals combined, they are less than infinity, but they are infinite.

I already said there is no more than one infinitesimal. Did you read my reply to you?

Actually, no.

If there is an infinitesimal at all, there are infinity of them. Look up hyperreal numbers. If (\frac{1}{\infty} = \epsilon) is an infinitesimal, then (\frac{1}{\epsilon}) is another infinitesimal an order of magnitude lower. There is no limit to how many times you can do this.

Can you have two infinitesimals be separated from each other? What would separate them?

Since nothing can separate one infinitesimal from another, just as nothing can separate one existence from another (what’s going to separate one existence from another…non-existence?) I believe the Infinite and the Infinitesimal are one and the same, just referred to differently. From our subjective point of view, the Infinitesimal is the Infinity/Existence that is in us (there is no non-existence in us) and the Infinite is the infinity/Existence that is outside of us (there is no non-existence outside of us). There is no inside the Infinitesimal and there is no outside the Infinite like there is inside us and outside us. There is us in Existence/Infinity and there is Infinity/Existence in us. Existence is in us are we are in it.

In the same way that 999…m and 888…m refer to the same thing, I think if what you have referenced refers to Infinitesimal, then it cannot refer to more than one Infinitesimal.

What separates infinitesimals ???

You’re kidding right?

Fucking values dude.

0.123412341234…

Is different than

0.111…

Like, what the fuck are you even talking about?!?!

And another thing, and this makes me laugh…

My argument against your argument for god is actually a better argument for god than your argument!! That makes me laugh at the irony.

If the addition of all infinitesimals are infinite but less than infinity, then there’s a superset there. Infinity is the superset. Of course when you add anything left of the decimal point, then it doesn’t work anymore.

I do have to give you an “A” for trying though.

Yikes dude.

(\frac{1}{\epsilon}) would be ({\infty}), not infinitesimally smaller than ({\epsilon})…
If you divide 1 by a tiny number, you get a huge number. The smaller the denominator, the larger the result.

But according to hyperreals, you could divide ({\epsilon}) by ({\infty}) and get an infinitely smaller value than ({\epsilon}), and so on, infinitely. So there really isn’t a lid on this whole “infinity/infinitessimal” business either way - as the terms would suggest. That’s why it’s pointless trying to assign a finite symbol to infinity/infinitessimal, because for any precision in what it denotes, it can always be bigger/smaller. Infinity is just a pointless concept for human conception. It can only be referred to in a handwavey “tends towards” way, such that it refers to finites getting really big or small to point us towards a precise finite result - such as with limits and calculus etc.

Sil… all that shit is ‘points towards’ / ‘estimations’

Equality? Fucking joke.

Good enough? That’s rational.

It points towards exactness, so it’s equal.

Trying to precisely quantify a difference is the joke.

Exact is a property of perceptual acuity. If we travel 6 miles away from a bolt on the sidewalk we can’t see it, if we use an electron microscope it is no longer a bolt.

Everything, everything in existence is not just the middle ground, it is “good enough”.

So nothing is strictly “equal”?

Mathematics seems to me to be the thought experiment of “what if precision were possible”. This is where the traditional split occurs between theorists and practitioners - when one prefers the aesthetics of either “what if it were precise” (e.g. math/logic) or “let’s just make it do something” (e.g. experimentalists/engineers). The latter accept “good enough”, the former do not.

There seems to be a clash of the two when it comes to relativity, where multiple perceptions occur depending on the point of reference, yet the mathematics allow a congruent consistency regardless.

I’m also reminded of fractals, where the degree to which you “zoom” into the detail affects a calculation - in the sense that strictly a perimeter might seem to be infinite, but a meaningful finite calculation is also possible when you don’t “zoom” in completely. A famous example of this would be the length of coastlines, or landmass perimeter.

“Identity” in general falls squarely into this dilemma, such as in the example you provide. The struggle to find utility is what humans seem primed to attempt - hence Experientialism, which distinguishes truth from utility. Whether or not it’s up to “perceptual acuity”, as you have coined, appears to be a matter of aesthetics. Mathematically, exact equality is permitted.

It’s an interesting thought experiment, but if things are exactly equal to each other, everything would be exactly the same… which is the same as nothing at all (which isn’t true). It’s all about utilitarian approximation

But that’s not what math does - it apportions things (i.e. rationalisation) such that inequality is everywhere, but proportional to everything else - allowing equality to be calculable via ratios. That’s why e.g. energy isn’t the same as mass, but it’s proportional in relation to the speed of light squared. They’re not exactly the same, but they can be expressed as exactly the same as a ratio of something else. That’s the utility of pure mathematics, as tested to a “utilitarian approximation” when scientific experimentation is performed. The two feed back on each other dialectically. It is indeed an interesting thought experiment for the very reason that its practical approximations really do have utility i.e. “science works”. It’s curious, no? That applied theory, despite its practical approximations when tested, actually works - and consistently too. It’s almost as if life can at least imitate precision, and maybe it’s just our attempts to test it that are the only imprecise element.

What do you mean separated? Certainly, if you believe that what separates 1 from (0.\dot9) is an infinitesimal, then you believe that what separates 2 from (1.\dot9) is also an infinitesimal. Yet they are separate by 1 whole number.

But what do you say about my comment about dividing an infinitesimal by infinity?

What is 999…m and 888…m?

Yikes, indeed! You’re so right, Silhouette. I sometimes make stupid mistaken, and that’s a clear example of one. But you got what I meant: (\frac{\epsilon}{\infty}).

Infinity just means “no end”. The confusion arises when the concept gets objectified (thought of like an object) and people confuse it for a number–the “biggest” number, the number farthest out on the number line–the handwaving you mention is a way of talking about infinity as if it were this number–whatever it is you’re calculating, we say it “tends towards” (i.e. gets closer to) that really big number. But I think a more accurate way of saying it is: it tends in the positive direction on the number line with no end.

double post