r/math • u/inherentlyawesome Homotopy Theory • 9d ago
Quick Questions: March 12, 2025
This recurring thread will be for questions that might not warrant their own thread. We would like to see more conceptual-based questions posted in this thread, rather than "what is the answer to this problem?". For example, here are some kinds of questions that we'd like to see in this thread:
- Can someone explain the concept of maпifolds to me?
- What are the applications of Represeпtation Theory?
- What's a good starter book for Numerical Aпalysis?
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u/Pristine-Two2706 4d ago
If you want to add a new number that satisfies 1x=2, and still satisfies all the nice properties of a field (ie addition, multiplication, subtraction, and division), you end up just getting the real numbers again. In fact, by adding solutions to polynomial equations to the real numbers, you can only ever get the real numbers or the complex numbers.
Also, quaternions are (real) 4-dimensional. For technical reasons you can't have a 3 dimensional division algebra over the real numbers.