A Hierarchy of Infinities

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Mathematics, Science
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11th Grade - University
•
Hard
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7 questions
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1.
OPEN ENDED QUESTION
3 mins • 1 pt
What does it mean that there are different sizes of infinity?
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2.
OPEN ENDED QUESTION
3 mins • 1 pt
How does the concept of infinity challenge our intuition in mathematics?
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3.
OPEN ENDED QUESTION
3 mins • 1 pt
Explain the concept of bijection in relation to infinity.
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4.
OPEN ENDED QUESTION
3 mins • 1 pt
How can we prove that the natural numbers and the even numbers are the same size of infinity?
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5.
OPEN ENDED QUESTION
3 mins • 1 pt
Describe how intervals on the real number line relate to the concept of infinity.
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6.
OPEN ENDED QUESTION
3 mins • 1 pt
What is the continuum hypothesis and why is it significant?
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7.
OPEN ENDED QUESTION
3 mins • 1 pt
What are the implications of the continuum hypothesis being independent of Zermelo-Fraenkel set theory?
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