You've raised a lot of great issues here. Let's try just the 1 + 1 = 2.

If one is going to conceive of one of something, what does that mean? It implies something is there having an identity and there is something more than that. We are talking quantity or counting. If we are counting, we are considering likenesses. That is, things are ordinarily different, but we are looking at only what they have in common. Before we go to any abstraction, let's look at apples. If you have one and then another, we define that combination as two apples. Adding is the combination of what we have considered together. So abstracting, 1 + 1 = 2 is the considering together of a likeness and another likeness.

That's a word definition in the real world. Not much mathematics. We may be talking symbolic logic if we are to go further into abstraction. Mathematics does have its foundations in philosophy as I've attempted here. If we skip foundations and go directly to math, we may talk about symbols such as "+" without regard to what they mean. We talk symbols and assume logical operations.

I will ramble on because there is more than one way to look at this. You say, "1+1 will always be 2." That is not any mystery if 2 is just the definition or shortcut for 1 + 1, just as 20 is the definition or symbol shortcut for 19 + 1.

If I recall, there is such a thing as "equivalence classes." If you look that up, things will rapidly get complicated, more so than you want to. In ordinary English I supposes it means if things are generally one way then each particular is going to be that way. Sometimes we can get another mathematical person on a forum who can explain it better, but that is mine.

Consider "two" pears. Then two pears will have the same "two-ness" as two apples. I'd better stop here.

My point is that mathematics as symbols is a simplification of larger consents that can not be completely understood without using mathematics terminology or symbols.

I am not confused about what math is and simply using mathematical terminology instead of the symbols isn't really explaining the reality of a situation not using math. Therefore, the conclusion can still be had that mathematics is just simple language used to understand farther complex concepts that we have no way of expressing with out numbers or other mathematics symbols/terminology.

I am not sure what you are trying to prove/argue here. I sounds like you are trying to teach me what math is which really isn't the question here and I don't understand why you would believe that I wasn't understanding what math is.

I understand that things get more complected when you start to realize that no to things are identical. However, using math is still simpler than trying to understand this reality without math. I am not saying math is away simple however, it is the simplest way to express some aspects of reality. This is why it is useful.

Calculus may not be simple however, it is much simpler to understand certain physical properties when you express them in Calculus therms.

Simply put Calculus based physics is my more intuitive than algebra based physics.

Calculus may be harder to grasp than Algebra however, understanding Calculus make understand many physical properties simpler.

I am not saying math is simple what I am saying is that math make communication simpler. As long as both people can understand the math than can intern understand the concept better. This is because as a language mathematics is far less open to interpretation than most language mediums.

Take English for an example. There is a rule that says that I always come before E unless its fallows C. This is a very wEIrd concept. In English there are exceptions for every rule and even exceptions the the exceptions. The simplicity to mathematics is there are no exceptions. There is only farther evolutions of the rules.

While it is completely possible that 1+1 may be closer to 3 than 2. Basically if you are rounding 1.49999999999999999+1.4999999999 your could still get 1+1=3. Because 1.4999999999+1.499999999 = 2.9999999999998 which rounds to 3 not 2. However, this is not actually an exception. In reality 1+1 will always =2 because 1.49999999999999 isn't actually 1 even if it rounds to (or is closer to 1 than 2.) This just means that in reality numbers are not normally as simple as 1+1. However, if you wish to be more concise you can be. All you need to do is look closer at the figure reality instead of rounding and making a guess.