How to prove that the new number produced by the Cantor's diagonalization process applied to $\Bbb Q$ is not a rational number ?

Suppose, someone claims that there is a flaw in the Cantor's diagonalization process by applying it to the set of rational numbers. I want to prove that the claim is false by showing that the new number produced by this process is not rational. How to prove this ? Hope I have made my question clear.
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I might have an approach that shows a counter example - where the flipped diagonal number produced is also rational. See: [Should a Cantor diagonal argument on a list of all rationals always produce an irrational number?](https://math.stackexchange.com/questions/677649/should-a-cantor-diagonal-argument-on-a-list-of-all-rationals-always-produce-an-i)
Despite replying to an old post, I would like to supplement things that that I missed out after reading all replies.

Fact:

1. $\pi$ is irrational

Cantor's technique for finding a contradiction has 1 property

1. The generated new number must be different

Cantor's contradiction makes sense because the new number is

1. Real number
2. Resulted from the aforementioned technique, which means its different from all enumerated real numbers

The contradiction will makes sense to $\mathbb{Q}$ if the new number is

1. Rational number
2. Resulted from the aforementioned technique, which means its different from all enumerated rationals

Here's the key. The very technique can give this number--$\pi$,

1. Rational number (***No***, it isn't)
2. Resulted from the method (Yes, it is different from all since its irrational)

This is how you conclude why is the generated number not necessarily rational, because the method gives a lot of freedom in picking the number