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Comment · 4 years ago
Comment · 4 years ago
Do integers exist? Do sequences of integers exist? If they do, so do the real numbers.

This is because any positive real number has a decimal expansion which determines it. For example pi = 3.1415926535... or 1/3 = 0.3333333...

Comment · 4 years ago
Comment · 4 years ago
Comment · 4 years ago
Comment · 6 years ago
At least for me, doing examples and computations is the best way to learn math, and also very important in research. Often an opaque general statement becomes clear after doing a few small examples. In linear algebra, I personally find some of the courses have too few computations, some concepts are best learned by working an hour by hand on some annoying 6 x 6 matrix..
Comment · 6 years ago
Your guess is as good as mine. My guess is that all intelligent life in the universe would be "soooo unique", not just the one on Earth. So it would be very improbable any life form would be similar to that on Earth.

However, it could be probable that there are two life forms in the universe which are similar. But then they would probably be too far apart from each other to ever be able to communicate.

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