During formal discussion, mental notes could help you maintain your focus/attention for the point that given by another speaker so you could give your opinion or counter argument later.
This will give the impression that you're an attentive and a competent person.
Yes, the Holocaust really happened.
There are still people who went through it and survived, alive today,
who have told their stories of it, thousands of times over.
And those who perpetrated it kept very detailed records of their own victims.
All of them are necessary
Hope my answer helped you :)
