A Line

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A line has formed at a box office to buy tickets. The first person in the line is a woman and the last person is a man. Prove that somewhere in the line there is a woman immediately in front of a man. (This is intuitively obvious, but give a careful proof using induction on the length of the line.)

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it would be easier to do by contradiction.

Rap

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Let there be N persons in the line, where N >=2. Let M be sucn an integer that the M-th person is the first male person in the line. Then, the (M-1)-th person is a woman immediately in front of a man.

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Re: A Line

RK4 wrote:

A line has formed at a box office to buy tickets. The first person in the line is a woman and the last person is a man. Prove that somewhere in the line there is a woman immediately in front of a man. (This is intuitively obvious, but give a careful proof using induction on the length of the line.)

Any proof merely transfers the intuition required to see that one person is in front of another, to one digit being in front of another.

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satt_fs wrote:

Let there be N persons in the line, where N >=2. Let M be sucn an integer that the M-th person is the first male person in the line. Then, the (M-1)-th person is a woman immediately in front of a man.

So, where's the contradiction here?

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RK4 wrote:

So, where's the contradiction here?

I didn't use condtradiction. Mine is a straightforward proof.

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Any proof merely transfers the intuition required to see that one person is in front of another, to one digit being in front of another.

You are not asking for proof. You are asking us to map body position to number position. Nothing is 'proved' by doing this.

Don't you understand what I am saying?

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Asking for proof in this example merely asks us to map the positions of people in the queue to the positions of signs in a sequence (numbers). Nothing is 'proved' by doing this.

Don't you understand what I am saying?

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The set of the persons in the line is "well-ordered", and hence the "first" male in the subset of persons of males makes sense.

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Re: A Line

RK4 wrote:

A line has formed at a box office to buy tickets. The first person in the line is a woman and the last person is a man. Prove that somewhere in the line there is a woman immediately in front of a man. (This is intuitively obvious, but give a careful proof using induction on the length of the line.)

If person n in the line is a woman, and there is never an instance of a woman being positioned directly in front of a man, it follows that person n+1 is also a woman. Since the first person in the line is a woman, it follows by inference that all persons in the line are women, including the last person in the line, should there be such a person. This is not compatible with the last person in the line being a man. Thus the conditions of the first person in the line being a woman, the last being a man, and there being no man in the line directly behind a women, gives rise to a contradiction.

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Proof is not true if if the line is full of say pets (dogs) or transvestites Smile

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Yes g___day got it right, this proof is only true if it is an either/or situation, but transvestites are ultimately male or female. Problems would arise; however, with eunuchs and hermaphrodites you can have a problem.

Moreover; many women and all female dogs can be bitches.

Rap

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Signing off this forum. Do not move this bloody post. Anyone nicks my ideas and its your arse.

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A Line

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