get2zpointer

To circumvent the one-party consent issue, he could just write a Terms of Service on the inside of his shirt that includes a clause about "Engaging in conversation as a use of the Services" that implies agreement with the Terms of Service.

It's not the infinity of the subset of Ramsey pairings that's the central point of interest in this proof. What is mainly interesting is that their proof can show this, using only finitistic methods. Their proof shows this without explicitly using any concepts of infinity, for example, without assuming an infinite superset.

It does not necessarily follow that if you disagreed with the media industry, you would not consume their products.

That's in a class of arguments that include statements like "If you disagreed with the use of your tax money, you would not pay taxes." Or "If you disagreed with the agricultural industry, you would not consume produce."

This is really dialed back. It seems Microsoft is pretty terrified of another Tay-like event.

Why is three better? In any family with k brothers, each male will have k-1 brothers, while each female (if any exist) will have k brothers. So the number of brothers in S(x) is gender dependent, despite the the third answer's claim that it isn't.