I don't understand why logarithms exist when we have exponential functions. Exponential functions seem to be an easier and less convoluted way to write something. Why invent logarithms to do something ...
Having a bit of difficulty understanding the conditional ($\rightarrow$) in mathematical logic. I read up on the already-existing questions and it did help me understand it better (the 'promise' ...
In the wikipedia page dedicated to conservative extensions, we find the following sentence: $T_2$ is a model-theoretic conservative extension of $T_1$ if every model of $T_1$ can be expanded to ...
I am curious how mathematicians came to develop complex exponentiation. How is the rule for complex exponentiation derived?
This is a basic question. I have a good intuition that $A$ is independent of $B$ if $P(A \vert B) = P(A)$, and see how you can easily derive from this that it must hold that $P(A,B) = P(A)P(B)$. ...
Typically, one doesn't just write down lists of axioms and then sees if there are enough interesting examples that satisfy them; they evolve over time, usually from a couple of very ...