Why the exponent must be a negative in the Fourier transform of any sequence? What happens with expressions
$$x(m)=\dfrac{1}{2\pi}\int_{-\pi}^{\pi}X(w)\exp(jmw)dw$$ if we define the Fourier transform of sequences as:
$$X(w)=\sum_{-\infty}^{\infty}x(m)\exp(jmw)$$ tal que $-\pi\leq w \leq \pi.$
recall that Fourier Transfrom of sequence $x(n)$ is $X(w)=\sum_{-\infty}^{\infty}x(n)\exp(-jnw)$
I am found that $x(m) = x(-m)$ this is true?