Miike012 said:The chapter I am reading is on proving limits... The terms "δ = min(δ1,δ2)" has came up a few times but what does it mean?
My guess is that the distances δ1 and δ2 are some where in the interval of the distance δ about some x value.
It's the other way around.Miike012 said:Ok it says the min of two numbers x and y is denoted min(x,y).. so I am guessing what I posted above that "min(δ1,δ2)" means δ1= δ if δ1<δ2 and vise versa. is that right?
The delta symbol represents the distance between the input value and the limit point in the limit definition. It is used to determine how close the input value needs to be to the limit point in order to have a desired output.
The value of delta is usually calculated by considering the constraints given in the limit definition. It is typically the minimum of two values, δ1 and δ2, which are determined by the given conditions of the limit.
The minimum function ensures that the chosen value of delta satisfies both conditions given in the limit definition. It guarantees that the input value will be within the required distance from the limit point, regardless of which condition is more restrictive.
The value of delta directly affects the accuracy of the limit proof. A smaller value of delta will result in a more accurate proof, as it will require the input value to be closer to the limit point. Conversely, a larger value of delta may result in a less precise proof.
No, the value of delta cannot be arbitrarily chosen. It must be determined based on the given conditions of the limit. Choosing an incorrect or arbitrary value of delta may result in an invalid or incorrect proof.