Proof Methods Proof methods Direct proofs
... • Proof: The only two perfect squares that differ by 1 are 0 and 1 – Thus, any other numbers that differ by 1 cannot both be perfect squares – Thus, a non-perfect square must exist in any set that contains two numbers that differ by 1 – Note that we didn’t specify which one it was! ...
... • Proof: The only two perfect squares that differ by 1 are 0 and 1 – Thus, any other numbers that differ by 1 cannot both be perfect squares – Thus, a non-perfect square must exist in any set that contains two numbers that differ by 1 – Note that we didn’t specify which one it was! ...
Full text
... addition exhibited irrational limits when summed over arbitrary infinite subsequences of N, by replacing n with a strictly monotone increasing function f:N->N. Owing to this factorial-like form, the argument employed in [7] was closely modeled on that of Euler's for establishing the irrationality of ...
... addition exhibited irrational limits when summed over arbitrary infinite subsequences of N, by replacing n with a strictly monotone increasing function f:N->N. Owing to this factorial-like form, the argument employed in [7] was closely modeled on that of Euler's for establishing the irrationality of ...
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... Conversely, let us start with a subset S of C such that S contains a non-zero complex number. Call any of the binary operations in condition 2 as well as the square root unary operation in condition 3 a ruler and compass operation. Call a complex number constructible from S if it can be obtained fro ...
... Conversely, let us start with a subset S of C such that S contains a non-zero complex number. Call any of the binary operations in condition 2 as well as the square root unary operation in condition 3 a ruler and compass operation. Call a complex number constructible from S if it can be obtained fro ...
Multiplying and dividing algebraic fractions
... Write improper algebraic fractions as mixed numbers using division or the remainder theorem. ...
... Write improper algebraic fractions as mixed numbers using division or the remainder theorem. ...
