- #1
RandomAllTime
- 26
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Hello everybody, I seek the analysis and criticism of mathematicians. I'm sure this has already been proven a while ago, but I wrote a proof that there is an infinite set of real numbers between any two real numbers provided they are unequal. I am not yet in college and I lack proper training in proof writing, so I come here to show you the proof and gather whether or not you think it is valid, or if it is broken and or needs revision. Thank you. Perhaps even my assumption is wrong. I am just a beginner who is trying to develop proof writing skills, so please excuse any trivial errors, but please do tell of them. Here is what I have come up with. It is quite short and simple.
Consider the closed interval [a,b], where a≠b and a,b ∈ ℝ.
Next consider the infinite sequence S =[/0], [/1], [/2], ... such that [/1] > a and limS = b.
The set of all terms in S shall be denoted X = {s|s∈S}
Since X is a subset of all the real numbers between a and b, and X is infinite, the set between any two real
numbers a and b is infinite.
Thank you.
Consider the closed interval [a,b], where a≠b and a,b ∈ ℝ.
Next consider the infinite sequence S =
The set of all terms in S shall be denoted X = {s|s∈S}
Since X is a subset of all the real numbers between a and b, and X is infinite, the set between any two real
numbers a and b is infinite.
Thank you.