Fraction Count-Up constant

The Fraction Count-Up constant is an irrational, Math Constant Discovered by JulianGutierrez2008 (it may have been discovered earlier but I could not find it) anyways, it's continued fraction is

1/(1+(1/(2+(1/(3+(1/(4+(1/(5+(1/(6+(1/(7+(1/(8+(1/(9...………..)))))))))) all the way up to infinity. It is approximately equal to 0.697774657964. It is called the 'count-up constant' because the number after the plus in it's continued fraction is going up by 1 each time. It can be seen on the Dree Encyclopedia Of Online Integer Sequences. Not much is known about it.

Why it's irrational (proof)
since it has endless fractions all with different denominators, in order for it to be rational, there has to be a number with every number as a factor, which cannot exist. so this number is irrational.

Further explanation
for example, the least common multiple of 4 and 9 is 36, so if you have to multiply/divide fraction with denominators 4 and 9, the answer would be a fraction with denominator of 36. for the FCUC, there is every number as a denominator (in the continued fraction), and there is no least common multiple of every number in existence. meaning the FCUC cannot be expressed with a fraction, meaning it is irrational.