How would you change this sentence to a true statement? -----

Some irrational numbers are also rational numbers.

--All irrational numbers are also rational numbers.--

--Half of the irrational numbers are also rational numbers.--

--One-third of the irrational numbers are also rational numbers.--
--Irrational numbers cannot be classified as rational numbers.--

Question

How would you change this sentence to a true statement?   -----

Some irrational numbers are also rational numbers.



--All irrational numbers are also rational numbers.--

--Half of the irrational numbers are also rational numbers.--

--One-third of the irrational numbers are also rational numbers.--
--Irrational numbers cannot be classified as rational numbers.--

anonymous · Answer

This question is answered in light of both math and linguistics.  The prefix "ir-" means "not".  So, even without mathematical knowledge, we have a dichotomy.  Either rational or not rational.  The math part:  rational #'s are expressed as p/q where p and q are integers.  Rational here does not mean "clear thinking".  It means able to be expressed as a ratio.  Ratio-nal.  So, putting the linguistics and math together, a number cannot be rational and irrational at the same time.

anonymous · Answer

well rational number is a number that can be defined as a ratio

anonymous · Answer

so an irrational number cannot be.

anonymous · Answer

a ratio... like pi or e

anonymous · Answer

i had to read that users comment like 4 times haha.. sounded like a text book

anonymous · Answer

some rational numbers are irrational.. but irrational numbers can never be rational.

anonymous · Answer

Nameless, you wrote "...some rational numbers are irrational.. but irrational numbers can never be rational..."  I hope you're joking!  You'll end up misleading someone saying things like that!  And pi and e are NOT rational!

anonymous · Answer

i said.. pi and e are irrational.

anonymous · Answer

just typed them on differnt lines.. cause i had a broken thought.

anonymous · Answer

Tcarro's answer to my question was correct.

anonymous · Answer

All right, if you combine two of your posts, but I hope you don't think that some rational numbers are irrational, because that comment of yours was contained all in one post.

anonymous · Answer

sorry, maybe i need to improve my posting skills.  my bad.. i mistyped that.  rational numbers are reperesented by a ratio. irrational numbers are not.  logically it is impossible for them to be the same.  tough crowd today.

anonymous · Answer

np