Recent content by Mike_bb

We can use empty product to define ##a^0=1##.

For ##a^0=1## we have symmetry around ##a^0##: ##\frac{1}{a^{-1}} = a## ##\frac{a^1}{a^{-1}} = a \cdot a## For ##a^0\neq1## we don't have symmetry then it's wrong case: ##\frac{a^0}{a^{-1}} = a^0 \cdot a## ##\frac{a^1}{a^{-1}} = a \cdot a## Thus, ##a^0=1##.

Ah, that's what you're talking about. :smile:

I don't understand again. ##a\cdot a\cdot a\cdot a^2## ##a\cdot a\cdot a\cdot a^1## ##a\cdot a\cdot a\cdot a^0## What is the next step?

When you wrote post#2 you probably meant that "to multiply number by no a's" = ##a*a*a*a^0##. I can't understand how did you infer that ##a^0=1## from this expression?

I can't understand how does it work if ##x*x*x*x^0##? x³ = 1 × x × x × x x² = 1 × x × x x¹ = 1 × x x⁰ = 1 (we multiply by x zero times, leaving just the starting 1)

This seems logical to me. But after rereading, your second post confused me: How is it possible "to multiply number by no a's"? I understand when ##1## is at the beginning (##1*a*a..a##). But as I understood you meant ##a*a*a*a*...*1##. Give me more details please. Thanks.

Hello! I decided to solve following equations: 1) Let ##2^x=0##: ##2^x=2^{2x}## and then ##x=0##. ##2^0=0## 2) Let ##2^x=1##: ##2^x=2^{2x}## and then ##x=0##. ##2^0=1## Could anyone explain how is it possible that ##2^0## has two values ##0## and ##1##? Thanks.

Hello! If theorems always work and they are true statements then why should we need to re-prove theorems that have been proved already by many people? Could anyone provide examples that confirm necessity of re-proving theorems? Thanks!

It should stay the same.

Thx. But I'm interested in the explanation that mentions empty product.

Could you explain how does it work? How is it possible to combine an empty product with original factors (see below)? Thanks. "The product of any factors combined with an empty product equals the original factors. Just as multiplying by ##1## does nothing, an empty product is treated as doing...

Why are you so sure?

Hello! I have problem in understanding why ##a^0=1##. I represent ##a^x## as ##1*a*a*a*a*...*a## (x times) Why ##a^0=1##? Why is ##a^0## not equal to ##0##? Thanks.

Spacetime curvature is geometric property.