Can someone explain each definition in detail for me. I want to fully understand

Question

Can someone explain each definition in detail for me. I want to fully understand it so can you break it down, especially the first one, not sure what it means with epsilon and the limits. Can you explain that one the most and every little part?

A sequence {xn} is said to be convergent to x Epsilon F if their is this is denoted by xn = x, or xn rightarrow x A sequence {xn} is monotonically nondecreasing if x1 Similar we can define {x} being monotonically nonincreasing if x1 strictly speaking, {xn} is montonically increasing if An ordered field said to have monotone sequence property if every monotonically nondecreasing sequence that has an upper bound converges. (is convergent)

Explanation / Answer

x E F means x belongs to F

Inverted A means " for all"

Opposite E means " there exists"

>= greater than or equal to

<= less than or equal to

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