2006-11-24 04:51:22 · 6 answers · asked by jenzilla84 1 in Science & Mathematics ➔ Mathematics
A possible proof:
It is easy to verify that AUB = A U (B-A). Since B is infinite and B is a subset of AUB, AUB is also infinite. However, A is finite, and if B-A is also finite then so is their union, which would lead to a contradiction (namely, AUB being finite and infinite at the same time), thus, B-A must be infinite.
By the way, after reading your previous question, I assumed that A and B were meant to be sets, not numbers.
2006-11-24 04:58:03 · answer #1 · answered by ted 3 · 1⤊ 0⤋
If B is infinite and we remove finitely many points
from B, B is still infinite. So removing all of A
from B still leaves an infinite set.
2006-11-24 12:58:58 · answer #2 · answered by steiner1745 7 · 0⤊ 1⤋
Suppose B-A is finite and equal to C
=>B-A=C
=>B=A+C
But B is infinite(given)
=>B cannot be expressed as a sum of 2 finite numbers as if the numbers are finite, the sum has to be finite.
Hence, our supposition is wrong.
=>B-A=~
2006-11-24 12:58:18 · answer #3 · answered by sushant 3 · 2⤊ 0⤋
Ok, say B is number "infinity" and A is the finite number of "2".
Infinity - 2=Infinity still.
2006-11-24 13:31:45 · answer #4 · answered by aaylasecura 2 · 0⤊ 1⤋
Even if you take away a finite quantity, an inifinite amount is still left over.
2006-11-24 13:16:51 · answer #5 · answered by ag_iitkgp 7 · 0⤊ 1⤋
okay,
infinite - finite = infinite
Even though that is theoretically impossible...how do you subtract a fixed value from an infinite value.
2006-11-24 12:54:49 · answer #6 · answered by Anonymous · 0⤊ 3⤋