Сan an Irrational number; like e, be equal to a second irrational number, π, times an integer, then divided by a second rational number? Such as: e = π a b , where a and b are some integers.

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Сan an Irrational number; like   e, be equal to a second irrational number,   π, times an integer, then divided by a second rational number? Such as:   e  =            π      a        b   , where   a and   b are some integers.

robegarj · Accepted Answer

Let   x  ,  y be irrational numbers, and   a  ,  b be some integers different from   0. Consider:      x    y    =      a    b  which is clearly equivalent to your question. If       x    y   is rational, then the answer is yes, you can find some integers   a  ,  b as above; otherwise, the answer is no. For instance, let   x  =      2  ,   y  =  3      2  . Then, you can write:  x  =      1    3    yRegarding this particular case, namely       e    π  , I think it is not yet known whether this number is irrational or not.

Erin Lozano · Accepted Answer

8    =  2      2    .More generally, any irrational times a rational gives another irrational.

Сan an Irrational number; like e , be equal to a second irrational number, π<!-- π -

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