# Why there is no Turing Machine that accepts the Diagonal Language? Given the diagonal language

$$L_d = {i: \sigma_i \notin L(M_i)}$$

Where $$M_i$$ are all Turing Machines and $$\sigma_i$$ are all the words, if you put in in a Matrix like this:

$$\begin{array} {|c|c|c|c|c|c|c|} \hline & \sigma_1 & \sigma_2 & \sigma_3 & \sigma_4 & \sigma_5 & …\ \hline M_1 & 1 & 0 & 1 & \dotsb & \dotsb & \dotsb \ \hline M_2 & 0 & 0 & 1 & \dotsb & \dotsb & \dotsb \ \hline M_3 & 1 & 0 & 1 & \dotsb & \dotsb & \dotsb \ \hline M_4 & \vdots & \vdots & \vdots & 1 & \dotsb & \dotsb \ \hline M_5 & \vdots & \vdots & \vdots & \vdots & \ddots & \dotsb \ \hline \vdots & \vdots & \vdots & \vdots & \vdots & \vdots & \ddots \ \hline \end{array}$$

Then $$L_d$$ is represented by the numbers in the diagonal of the matrix. In class I was told that there is no TM that accept $$L_d$$, but I do not quite understand why is that, could somebody help?

PS: The above explanation was included because I did not know if this is called Diagonal Language in English, Spanish is my mother tongue. Posted on Categories proxies