It is always stated that e, defined as the limit as x goes to infinite of (1 + 1/x)^x, is an irrational constant. Similarly, it is stated that pi is an irrational constant. Probably, there are others too which I am less familiar with. Is the fact that these numbers are irrational assumed, or can it actually be proved that they are irrational?
2007-01-03 20:17:31 · 6 answers · asked by G A 5 in Science & Mathematics ➔ Mathematics
One definition of "rational" is that the decimal either terminates or repeats. How do we know that these constant neither terminate nor repeat?
2007-01-06 00:49:41 · update #1
I am not very sure for all put some of them say pi . e and sqrt(2) can be poved to be irrational.
proof that sqrt(2) is irartional
http://en.wikipedia.org/wiki/Irrational_number#The_square_root_of_2
proof that e is irrational
http://en.wikipedia.org/wiki/Proof_that_e_is_irrational
proof that pi is irrational
http://www.lrz-muenchen.de/~hr/numb/pi-irr.html
2007-01-03 20:51:48 · answer #1 · answered by Mein Hoon Na 7 · 2⤊ 0⤋
it can actually be proven. If you really had a lot of time, you could calculate pi to the nth place(after about 30, i gave up).
any irrational constant is:
a) not rational (aka a ratio)
b) does not change
c) is not defined by measurement, but of a state of being what it is.
2007-01-11 16:05:55 · answer #2 · answered by Brian F 4 · 0⤊ 0⤋
An irrational number cannot be expresssed in the form of P/Q, P and Q being rational numbers and Q is not equal to zero.
There are infinite irrational numbers between two rational numbers in the number scale.
2007-01-03 21:22:48 · answer #3 · answered by Pearlsawme 7 · 1⤊ 2⤋
The basic idea is that they can't be written as a fraction. 7.2 is just 72/10, so that's rational. e and pi can't make that claim. A more substantive characteristic may exist but is beyond me.
2007-01-03 20:27:01 · answer #4 · answered by oasisfan_fatstrat 1 · 0⤊ 0⤋
they can be proved irrational generally by contradiction
proof that e is irrational is given on wikipedia
2007-01-03 20:32:16 · answer #5 · answered by Anonymous · 2⤊ 0⤋
Mathematical constants can not be changed at all, for so many years ever since and before we started schooling they we stated like that so nothing can be done to improve because the books are worldly spread no matter what new science is coming in no change to those mathematical concepts.
2007-01-03 20:42:53 · answer #6 · answered by ConRob 2 · 0⤊ 4⤋