


How has the understanding of rational and irrational numbers evolved over time? What are some current areas of research involving rational and irrational numbers?
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what's the difference between rational and irrational numbers Informational
- How do rational and irrational numbers relate to the study of mathematical sequences and series? Can a series with rational terms converge to an irrational number?
- Do mathematical games ever involve strategies or outcomes that depend on the rationality or irrationality of numbers? How do rational and irrational numbers relate to the concept of mathematical intuition?
- What is Lebesgue measure, and how does it treat sets of rational and irrational numbers? What is the Dirichlet's approximation theorem, and how does it relate to rational approximations of irrational numbers?
- Are all transcendental numbers Liouville numbers? Are there irrational numbers that are not transcendental?
- Are there number systems beyond the real numbers where the concepts of rationality and irrationality might be different or extended? What are p-adic numbers, and how do they relate to rational numbers?
- What are transcendental numbers? Are all transcendental numbers irrational?
- What happens when you try to express an irrational number as a fraction?
- How do rational and irrational numbers relate to the concept of infinity? Can you have different "degrees" of irrationality?
- Can irrational numbers be expressed as a fraction?
- Is the sum of two rational numbers always rational?
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