500 prompts matching "Prove command word: line does not intersect a curve"
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Show All Working: Evaluating a repeated operation such as a*(b*c)
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Learn: What closure means for a binary operation
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Worked Example: Testing the even numbers for closure under addition
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Explain Back: Testing the integers for closure under division
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Learn: What it means for an operation to be commutative
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Worked Example: Testing a*b against b*a for a given rule
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Explain Back: What it means for an operation to be associative
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Worked Example: Testing whether star distributes over plus
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Explain Back: Showing distributivity fails by a counter-example
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Show All Working: Using distributivity to simplify an expression
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Learn: What an identity element is
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Worked Example: Finding the identity element from a rule such as a*b = a + b - 3
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Explain Back: What an inverse element is
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Show All Working: An element with no inverse under a given operation
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Worked Example: The law for multiplying powers of the same base
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Explain Back: The law for a product raised to a power
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Show All Working: Simplifying an expression with letters and indices
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Learn: Why any non-zero number to the power nought is one
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Worked Example: Rewriting a negative index as a fraction
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Explain Back: A fractional index with a numerator above one
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