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As many real numbers between (0,1) as there are between (1, infinity)? Doesn't add up!

I don't know if there's an obvious answer to this question but.. as any real number from (1, infinity) can be related to a specific real number from (0,1) as => (1, infinity) = 1/{specific real no from (0,1)} Which implies the statement in the title above.. that can't be true because of course the number of real numbers from (0,1) is equal to number of real numbers from (1,2) alone which implies that number of real numbers from (1, infinity) >> number of real numbers from (0,1).. which proves a contradiction... Does that means there's a flaw in the foundation of mathematics?

submitted by /u/sucidalwithADHD
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from math http://bit.ly/2HK44l6
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