I've always used equations, but some time ago i have started to ask myself "why the heck can i pick 2 things, put a = between them, and get to conclusions?".

I've thought about the following, please, correct me if i am wrong. Tell me if this is a correct explanation for equations.

I say X+1 = 5

when is this true?

exactly when X+1 is 5

and i think "okay....but how does that help?" it could, but i dont want to know how much X+1 needs to be, i just want to know how much is X

then i think

if i say X+1 = 5, then i can remove 1 from both sides and will get an equivalent sentence.

I do it

X+1-1=5-1

i get X=4

what does that mean?

X+1 = 5 is true if X=4

Tell me if i am correct up to this point.

Now i thought about another theory

X+1=X

i apply me previous idea, and i get

0=1

what does that mean?

it means that X+1 would equal X if in my universe 0 was the same as 1

well, i could create my own universe in which 0 equals 1, but i want to me in the numbers universe, so i wont accept that solution, and so there isn't any other.

Did i do anything wrong in my reasoning? Please tell me, i'm no mathematician, and this problem is killing my brain, i need to explain equations.

Thanks in advance