Pascal's statement, known as Pascal's Wager, was put by French philosopher, Blaise Pascal. He said that even though the existence of God cannot be established by reasoning, a person should "wager" as though God exists, because by so living he or she has potentially everything to gain and nothing to lose. It was an appeal to self-interest, making belief rational, rather than necessarily logical.
An Alternate view:
Pascal's Wager, of course, depends on there being only two choices - no god, or his God. This is called basing an argument on a "False Dichotomy", saying the range of choices is limited to two when there are more potential options available. Of the several thousand gods worshipped throughout human history it is difficult to imagine a process to choose the "right" one. Even more difficult would be the process to imagine how to believe in this deity - does it require circumcision, blood sacrifices, or dietary conformity. Also one would have to hope the deity chosen offers some sort of eternal reward, not all of them do. Another consideration would be the consequences of choosing the wrong god. Some of them are pretty testy if you make a bad choice. Too bad if you are wrong!
The wagers results then become:
1. If you choose a god with an associated afterlife and he/she/it exists and cares anything about you (another question) and you are right in your choice you may get your "reward" if you haven't ticked him off by not following all the rules or by just believing in he/she/it with the ulterior motive of getting a reward. Note that not all afterlife's are pleasant even for the "good".
2. In the same case as above, and you choose to ignore this god/afterlife package, you probably wind up in a comparable situation - maybe a bit worse, maybe a bit better.
3. If there is no god, no afterlife, no continuation and you wasted your time mutilating yourself and your kids, eating a restricted diet or giving your time and money to a ragtag bunch of shaman's, you've missed a lot in this life - the only one you've got.
4. If case 3 is true and you live a normal life with no effort made to believe in any god or follow any "divine" rules - you win.
To prove by contradiction, you assume that an opposite assumption is true, then disprove the opposite statement.
To prove that if (r) is rational and (x) is irrational, then both (rx) and (\frac{r}{x}) are rational, we can use the fact that the product or quotient of a rational and an irrational number is always irrational. Since (r) is rational and (x) is irrational, their product (rx) must be irrational. Similarly, the quotient (\frac{r}{x}) must also be irrational. Therefore, we cannot prove that both (rx) and (\frac{r}{x}) are rational based on the given information.
It must be a generalised rational number. Otherwise, if you select a rational number to multiply, then you will only prove it for that number.
It is not possible to prove something that is not true. The square of 2 is rational, not irrational.
It is what you are trying to prove
opposite
To prove a statement false, you need ONE example of when it is not true.To prove it true, you need to show it is ALWAYS true.
No, despite common belief, a doctor cannot prove that your a virgin.
To prove a statement by contradiction one begins by assuming the statement is not true. Contradiction is the act of giving the opposing something that you feel is not right.
My definition of proving something would mean to ensure belief or trust into another person's mind. To have factual or true proof when supporting your statement; enough to persuade their judgment.
pi is irrational so that's impossible
No, they are not. 1/2 is a ratio of two integers and so it is rational. But it is not a whole number.