Mathematics: I'm 20, my dad is 50. After an infinite amount of time, will he still be older than me?

Time is generally modeled as a real number, or perhaps as a positive number: age since the big bang, so "after an infinite amount of time" has no defined meaning. In mathematics sets can be infinite (if they can be placed in one-to-one correspondence with a proper subset of themselves), but "infinity" is not a value you can do algebra on. When you define operations on sets and make groups or fields like the real numbers, "infinity" is not an element of the set and so cannot be "added". There are a few cases where you might try to do this explicitly, e.g. the Riemann sphere, which is the complex numbers plus a point "at infinity" which has the topology of a sphere. However in such cases "after an infinite amount of time" still doesn't make sense.

This brings up a physics question: what is the shape of space-time. In special relativity, time is sometimes modeled as a "4th dimension" and in general relativity, gravity is expressed as a local curvature of space time. Many theories exist about the global shape of space time, but we don't really know.   
On a more human note, you are talking about the age of living people. People's lives are a segment of time. You are born, your age increases while you are alive, and then you die. After people die, people generally say things like "he would have been 92 years old this year", because we don't think you get older after you die. If you change the question to "I was born in 1995 and my dad in 1965. After an infinite amount of time who was born first?" Then the "after an infinite amount of time" is irrelevant, which trumps its meaninglessness. If one event happened before another, the passage of time does not change this.

I'd like to hope that the universe will expand for a while, then stop, then contract, so that time started with a big bang and will end with a big crunch, so that "after an infinite amount of time" the universe explodes again and the process repeats. But I doubt anybody in some kind of  "next" universe knows or cares who you, your dad, but assuming there is some kind of super-univeral way to answer those questions, you would still have been born after your dad.

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