How do we know when we are allowed to use transfinite induction in a proof?
Edit: considering the replies, I should say the following:
Consider an infinite sum of fractions.
By induction we can show that for any finite step of this sum we get another fraction. However the infinite sum (step at $\infty$) might be irrational.
So we cannot use induction till ordinal w / cardinal $\aleph_0$ / infinity.
Similarly I ask when we are allowed (or not allowed such as in the example above) to use transfinite induction.
I appreciate the answers and they are not 'wrong' but I don't think they address this, hence the edit. My apologies for not being clear enough.