Key Introduction What is a Quadratic Equation?
... Algebra - Rearranging and Solving Quadratic Equations The quadratic formula states that for a quadratic equation of the form y equals ax squared plus bx plus c, the value of x is equal to negative b plus or minus the square root of b squared subtract 4ac, all divided by 2a. For example, for the quad ...
... Algebra - Rearranging and Solving Quadratic Equations The quadratic formula states that for a quadratic equation of the form y equals ax squared plus bx plus c, the value of x is equal to negative b plus or minus the square root of b squared subtract 4ac, all divided by 2a. For example, for the quad ...
Cardinals 1. Introduction to Cardinals We work in the base theory ZF
... then 2κ = κκ = κcof(κ) = (גκ). In the singular case, note that 2γ = 2<κ ≥ κ. Thus, (גκ) = κcof(κ) ≤ (2γ )cof(κ) = (2δ )cof(κ) = 2δ = 2γ (where cof(κ) < δ < κ). Thus, 2<κ · (גκ) = 2<κ . If κ is regular, then 2<κ ≤ 2κ = κκ = (גκ). So, 2<κ · (גκ) = (גκ). In either case, 2κ = 2<κ · (גκ). F ...
... then 2κ = κκ = κcof(κ) = (גκ). In the singular case, note that 2γ = 2<κ ≥ κ. Thus, (גκ) = κcof(κ) ≤ (2γ )cof(κ) = (2δ )cof(κ) = 2δ = 2γ (where cof(κ) < δ < κ). Thus, 2<κ · (גκ) = 2<κ . If κ is regular, then 2<κ ≤ 2κ = κκ = (גκ). So, 2<κ · (גκ) = (גκ). In either case, 2κ = 2<κ · (גκ). F ...
