Mike_bb's latest activity

Could you explain how does it work? How is it possible to combine an empty product with original factors (see below)? Thanks. "The...

In arithmetic, ##x^k## is defined recursively. The recursive step is ##x^k=x^{k-1}x##. What is the base case then, ##x^0##? For the...

$$a^x:=\exp(x\ln a),\quad \exp(x):=1+\sum_{k=1}^\infty\frac{x^k}{k!},\quad a>0$$

##a^0## can't be ##0## because if ##a^0=a\cdot 0 =0## for every ##a##, then ##0^0=0##, that is not true in mathematics ... In addiction...

Space-time curvature.

This can only represent "gravitational fields" on the chosen background. It can't, for example, represent a black hole spacetime...

This has several excellent answers and I cannot improve on them. I just have this persistent nagging voice wanting to express this...

Very similar to post #6. $$ a^0=a^{x-x}=\frac{a^x}{a^x}=1 $$

And once there is some actual evidence supporting your preference then it will be an acceptable topic for PF. But even then it would be...

Why are you so sure?

We are already in that situation with GR alone. So why should we hypothesize about unknown possible future theories when we can already...

Exponents are about multiplication, and 1 is the multiplicative identity. If exponents represented repeated addition the zeroeth power...

I won’t argue against that. In either case, the local gravitational force, like fictitious forces, is not measurable either way. It can...

Another way to look at it ##a^0 = 1## ##a * a^0 = a * 1## ##a^1 = a## Of course you can reverse the steps and conclude that ##a^0...

##a^0=a^1a^{-1}=a\frac{1}{a}=1##