Why does adding up a bunch of numbers and dividing that figure by the amount of numbers equate to an average?

That's the point I'm making, brainlet.

We get to a point where mathematical concepts can only be justified by themselves.

2+2=4

Well, how do you know that?!

Well because:

2+2=4 or I have two objects and another two objects and together they make something which I define as four.

I am not saying we shouldn't use mathematics. Only that we should realise the groundlessness of our beliefs.

We get to a point where things can only be justified by themselves or we have to repeat their definition.

Stop thinking of Mathematics as a God and realise it has its groundlessness like many other beliefs.

You are correct. It works for us, but I simply want to point out the groundlessness in our believing.

Welcome to Mathematics*

Its just a way if creating a number that is very representative of the values as a whole.

You are absolutely right.
Mathematic does not rely on infinite proofs. Rather, it is based on axioms and postulates.
Axioms are the absolute level zero on which all math is based upon. They are considered to be self-evident and they cannot be proven relying on other mathematics. Axioms are also extremely rigorous in their definition in order to avoid confusion and paradoxes.
Postulates are things which are considered to be treated and which cannot be proven right or wrong. However, their acceptance is necessary if you want to move further into the topic. For example:
If you accept Euclid's 5th postulate then you are doing Euclidean geometry. If you don't, you are in non-Euclidean geometries. Both are extremely different and theorems that apply to one may not apply to the other.

>Stop thinking of Mathematics as a God and realise it has its groundlessness like many other beliefs.
Not that guy, but I think we start getting into philosophy at that point.
>What does it mean to "define"?
>Is what man defines as something universal?
>Are any definitions or truths ever universal?
>Can human definitions capture the true essence of a thing?
>Can the essence of a thing even be understood actively?

Like, sure at it's roots it may seem groundless, but we're working with human constructs that help us to [math]kinda[/math] understand the "truths" of the universe, and that human construct happens to be math.

>Welcome to Mathematics*
I am this guy though, and I gotta ask, how much does your Autism hurt on a daily basis?

Truth is belief, friend!

>All you are stating is that an average is an average. You're just repeating the definition.
Can you read? You asked what the average is and he answered:
>It's a generalization of finding the middle of two points.
It's the "middle" of the numbers, weighted based on the size and frequency of each number. Other types of averages exist that depend on different weightings and correspond to new "middles". But this actually is a huge open question in statistics. What is the "right" value to use as your measure for the "middle"?

The average of n number is the number M that multiplied by n (i.e. summed n times) gives the same result as summing all n numbers

of n numbers*

2 values divided by 2

Good question. It is a philosophical question however, not a mathematical one. To understand what an average is, we first need to understand a few more base concepts, namely:
Measurement, Number or value, and Unity.
Lets talk about real measurements, in an attempt to make numbers less abstract. The most basic thing you can measure is the amount of something. How many of something do you have? Lets say you are building a brick house. You want a simple way to communicate how many bricks you need for one row of a particular section of the wall. You hold up one finger for every brick you want. For every brick you need you hold up one finger. Another person can easily see how many fingers you hold up and bring you one brick for every finger. Without using numbers you have used measurement and unity. The one finger is unity. It does not matter in what order you picked your fingers to represent bricks. The fingers are interchangeable. One finger any finger corresponds to one brick any brick. The measurement is how many fingers you hold up. It is a group of identical units. Numbers are a way to represent unity and or groups of unity, that is measurements. A measurement is the mapping of a real world amount of something to a symbolic representation of that amount.
What is AVERAGE then? Lets say you are working on three walls. One is 7 bricks long one is 11 bricks long and one is 9 bricks long. You have your assistant bring you all those bricks. in total you get 27. Your assistant wants to carry these bricks in just three equal loads. As luck would have it, 27 divided by 3 is 9 and nine bricks can be carried at one time. They carry one pile of bricks next to each of the three walls. You start to lay the bricks on the respective walls. The first wall gets 7 bricks and the 2 you lay on the next row above these. The second wall get 9 bricks and 2 are missing. The third wall get all 9 bricks that it needs. You look around, and you see what average means.

You can use the median instead.

Fuck off OP.

>Baby's first discovery of axioms

You didn't event attack it from the inductive fallacies of math

Funny coincidence was that 2 days ago I came up to similar question.

Another funny question (not related) is:
Statement S is T
So it's negation is F
So it's negation's negation is T again

Why does double negative equal positive? Explain please using mathematical language.

-(-1)=1

If I'm correct in assuming that you have to evaluate the statement to a number before you do the negation, then T can be considered a number for the duration of the negation. F is the result of negation thus also a number. When you negate F you get T. Understanding why negation reverses itself when done to a number is trivial. The problem arises when we negate the statement not the value of the statement. It is still true that negation reverses itself, but proving why, would be more difficult. I'd need to know exactly what a statement can and can not be. But I refuse to do so if I can't use a bricklayer in my examples and a narrative style.

>Is it another made up mathematical concept?

Yeah pretty much. What's your point?

>2+2=4
>because 2+2=4
t. brainlet who has never heard of Peano axioms.

It's just bullpoo.

>We get to a point where mathematical concepts can only be justified by themselves.

yeah no shit it's called an axiom

What if he wants a mode?

I have never had the mode come in useful before. The median is nice since it resists being influenced by outliers, unlike the average.

But I suppose he could use the mode if he would like.

>Why does double negative equal positive?
That's actually a good question. And the answer is that... they don't generally. For them to be equal you have to accept law of excluded middle, that is, that each statement is either true or false. A OR NOT(A) = True. This law might seem obvious at first, after all, what else can statements be in binary logic? But let's for now just suppose that we do have it, as common sense and classical logic dictates.

Look at the statement NOT(NOT A). If A is true, NOT A is obviously false, as there can't be anything else. Denote NOT A as X. As X is false, NOT X is true. Therefore, if A is true NOT(NOT A) is true. Same reasoning applies when A is false. So, NOT(NOT(A)) always equals A if we include law of excluded middle.

I put so much emphasis on law of excluded middle because some logicians use theories without it. Why would they do that? Imagine situation: a mathematician researches some object O. He wants to know if such object exists. Basically, he wants to prove the following statement S: "object O exists". He tries proof by contradiction. That is, he assumes NOT(S) and shows that it leads to contradiction. Therefore it is false and the opposite, NOT(NOT(S)) is true. Now, in classical logic NOT(NOT(S)), as we've just shown, it's equal to S. We've proved that object O exists... but can we show it? How can we do anything with it? Maybe it "exists", but there is no way for us to "construct" it? In thisbcase, can we really say that it actually exists? We just don't know. Interpretation of NOT(NOT(S)) is "O can't not exist" and without law of excluded middle we can't bring it down to "O exists". Some mathematicians want more concerete, constructible results. That's why they reject law of excluded middle and such logic without it is called constructivist logic.

tl;dr shit's cray yo, why can't there just be peace y'know

you DISGUSTING BRAINLET
do you NOT KNOW how many pages of PROOF it takes to prove ONE PLUS ONE EQUALS TWO????????

HOLY shit go back to COMMUNITY COLLEGE

>Is it another made up mathematical concept?
yeah lol

[math]2 + 2 = S(S(0)) + S(S(0)) = S(S(S(0))) + S(0) = S(S(S(S(0)))) + 0 = S(S(S(S(0)))) = 4

All mathematics is made up. An extremely small fraction of it accidentally can very roughly describe the world we live in.

you haven't defined what "2" or "+" is, let alone "2 + 2 = 4"

come back when you can do that from the logical foundations and rigor we mathematicians require

Assume peano axioms. Define + and natural numbers as it's usually done. 3-4 pages maximum. Unless you want me to write whole monography about predicative logic first.