But why is there no quintic formula? by MathKiwi
. Source. 10 minutes, that's about the right length, well done.Like the rationals, this field also has the same cardinality as the natural numbers, because we can specify and enumerate each of its members by a fixed number of integers from the polynomial equation that defines them. So it is a bit like the rationals, but we use potentially arbitrary numbers of integers to specify each number (polynomial coefficients + index of which root we are talking about) instead of just always two as for the rationals.
Each algebraic number also has a degree associated to it, i.e. the degree of the polynomial used to define it.
TODO understand.
Sometimes mathematicians go a little overboard with their naming.
Bibliography:
There's a billion simple looking expressions which are not known to be transcendental numbers or not. It's cute simple to state but hard to prove at its best.
Open as of 2020:
Bibliography:
- www.quantamagazine.org/recounting-the-history-of-maths-transcendental-numbers-20230627/ How Math Achieved Transcendence by David S. Richeson (2023).
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An algebraic equation is a mathematical statement that expresses the equality between two algebraic expressions. It involves variables (often represented by letters such as \(x\), \(y\), etc.), constants, and arithmetic operations, such as addition, subtraction, multiplication, and division.