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The point being that we fundamentally can't assert true same-ness; incompleteness fundamentally doesn't allow it. So, even same-ness is subjective, often a bit fudged from abstract ideality for the same of simplicity.

In short, my point here is that same-ness doesn't truly require absolute equal in all conceivable senses, but rather in all senses that we care to appreciate.

The point being that we fundamentally can't assert true same-ness; incompleteness doesn't allow it. So, even same-ness is subjective, often a bit fudged from abstract ideality for the sake of simplicity.

In short, my point here is that same-ness doesn't truly require absolute equality in all conceivable senses, but rather in all senses that we care to appreciate.

###Summary: Equality is context-subjective, sameness isn't so much.

###Technical point: Even identity is subjective, despite being less subjective than equality.

1+1 and 2 are different despite being equal because we can tell them apart; for example, we write and pronounce them differently. Because we can appreciate that these differences exist, 1+1 and 2 are different things despite being equal.

However:

1. What about 1+1 vs. 1 + 1; are they different?
   I mean, yeah, technically. For example, this post is stored in digital format on a StackExchange server, and there's a meaningful physical difference between 1+1 and 1 + 1 in the physical world.

2. What about 1+1 vs. 1+1; are they different?
   Again, yeah, technically. For example, while editing this answer, if I tried to delete one vs. the other, the result would be observable. So they're different in that they appear in different contexts.

3. What about 1+1 vs. itself a second later?
   This is, I'm now referring to the exact same string that appears earlier in this paragraph, stored in the same location on the same computer – but, at slightly different times. So is that different? (Related question.)

Again, yeah, technically... if we care to make that distinction. I mean, we could refer to it as a different thing at different moments in time, if we reallllly wanted to...

4. What about 1+1 and itself at the same moment in time?
   Well, now there might, in theory, be some sort of difference, but it's hard to say what that might be. For example, maybe we're living in The Matrix, and when we think about that same thing in different ways, our brains are being altered in ways we can't perceive such that our thoughts map to different concepts beneath our level of perception.

But even if we can't verifiably perceive differing notions of potential distinctions, we can imagine them, then consider the abstraction in which they might exist.

And now we're completely off in Crazytown, right? Like, each step of the way above, we got more-and-more pedantic, with increasingly minor distinctions to the point that we started considering abstraction descriptions that'd only make sense if we seriously regard hypothetical brain-in-vat scenarios.

The point being that we fundamentally can't assert true same-ness; incompleteness fundamentally doesn't allow it. So, even same-ness is subjective, often a bit fudged from abstract ideality for the same of simplicity.

In short, my point here is that same-ness doesn't truly require absolute equal in all conceivable senses, but rather in all senses that we care to appreciate.

###Summary: Equality is context-subjective, sameness isn't so much.

A = [ 0, 1, 2, 3 ]
B = [ 1, 2, 3, 0 ]

* I ordered their items because I needed to to write them down.  However, if they're unordered sets, then my choice to write their members down in different orders wouldn't reflect an actual distinction between them.

A = [ 0, 1 ]
B = [ 1, 0 ]

* If they're [**_ordered_**](https://en.wikipedia.org/wiki/Ordered_pair), then the differing orders are a meaningful distinction between them.

* If they're [**_unordered_**](https://en.wikipedia.org/wiki/Unordered_pair), then the differing orders aren't a meaningful distinction between them.

In general, things are the same if we can find no meaningful distinction between them. This is a stronger condition than mere equality, as we'll often describe different things as being equal (examples in next section).

###Examples of non-same (different) things that're equal.

This section provides examples to help showcase the distinction between same-ness and equality.

In general, two things are the same thing only if they're indistinguishable in all appreciated respects; this is, things are the same if we literally can't identify an appreciable manner in which they're not he same. However, it's easier for things to be equal; we often consider things to be equal even when they're not the same.

Examples:

1. In math, the expressions 1+1, 2, 3-1, 10/5, etc., are equal despite not being the same expression.

2. In law, Bob and Suzy are equal under the law despite not being the same legal person.

3. In physics, a force and its equal-but-opposite reaction are equal despite not being the same physical action.

4. In C# programming, different object's can still be .Equal().

* For example, [this C# program](https://dotnetfiddle.net/1m1qYK) assesses if two `object`'s are the same _and_ if they're equal, finding that they're different-but-equal.

 >     using System;
>                       
>     public class Program
>     {
>       public static void Main()
>       {
>           var a = "Hello!";
>           var b = (" " + a).Trim();
>           
>           var areSameMessage =
>                       "Objects 'a' and 'b' are "
>                   +   (System.Object.ReferenceEquals(a, b) ? "the same" : "different")
>                   +   " objects."
>               ;
>           
>           var areEqualMessage =
>                       "Objects 'a' and 'b' are "
>                   +   (a.Equals(b) ? "equal" : "not-equal")
>                   +   " objects."
>               ;
>           
>           Console.WriteLine("a:\t\"" + a + "\"");
>           Console.WriteLine("b:\t\"" + b + "\"");
>           Console.WriteLine(areSameMessage);
>           Console.WriteLine(areEqualMessage);
>       }
>     }

 which prints

 >     a:    "Hello!"
>     b:    "Hello!"
>     Objects 'a' and 'b' are different objects.
>     Objects 'a' and 'b' are equal objects.

1. In money, 1 Euro is currently equal to about 1.09 US dollars despite these being different amounts of different currencies.

In all of these examples, the point's that we can assess different things as being equal in some sense despite them not being the same thing.