Hello! Feel free to post anything vaguely math related below this topic. I am making this out of boredom, so I hope you have fun. I myself only know basic calculus so that’s about all I can assist with(i.e. simple differentiation, limits, logarithms, etc.) Post anything math related that you want though. Have fun!
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I guess I’ll start. Maybe a fun cubic equation,
\displaystyle{ 2x^3-5x=3 }
or summation problem:
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This statement of yours is largely false, and can be quite easily disproven using a variety of differing methods.
For my proof, I will be referring to and using the Peano Axioms (Peano axioms - Wikipedia), which are a set of propositions that attempt to standardize standard arithmetic.
Firstly, Peano’s first axiom states that “the constant 0 is a natural number”, and as such, 0 is a natural number by definition. The second axiom states that X=X, meaning equality is reflexive. As such 0=0, by definition. Axioms 3 and 4 follow, “x=y,y=x” and “x=y,y=z,x=z” allow us to know that equality is both symmetrical and transistive between numberss. Axiom 5 states “For all a and b, if b is a natural number and a = b, then a is also a natural number. That is, the natural numbers are closed under equality.”.
Axiom 6 states that for any natural number n, S(n) will also be a natural number, where S(n) represents the successor of the number. Axiom 7 states that if S(m)=S(n), then m=n. And axiom 8 states that no numbers successor is 0. With this, we can define addition.
We can define addition as follows->
for b=/=0: a+S(b)=S(a+b)[1]:a=0=a[2], for example
a+1=a+S(0) (by definition 1 is successor of zero and addition is reflexive)
a+S(0)=S(a+0) (by definition of addition) [1]
a+1=S(a) [2]
1+1=
1+S(0)= (definition of 1)
S(1+0) [1]
S(1) [2]
S(1)=2 (by definition)
edit: I guess I have to prove that 2 =/= 3 but my brain is too smooth for that.
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Next: 3+2^7*24=?
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3+(2^7)*24 or 3+2^(7*24)
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both (rip min. 10 characters)
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