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4meonly: Legendary Member; Posts: 891; Joined: Sat Aug 16, 2008 4:21 amFollowed by: 1 member; Thanked: 27 times; GMAT Score:660(

by 4meonly » Sun Jan 18, 2009 8:35 am

Guys, why 0! = 1?
What positive integer is befire zero?

And why 0^0 has no value?

I just want to understand this

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Source: Beat The GMAT — Quantitative Reasoning | Sun Jan 18, 2009 8:35 am

DanaJ: Site Admin; Posts: 2567; Joined: Thu Jan 01, 2009 10:05 amFollowed by: 550 members; Thanked: 712 times; GMAT Score:770

by DanaJ » Sun Jan 18, 2009 8:46 am

0! = 1 because some guys interested in math thought they should just have that rule a long time ago (we call it a convention in RO, but I'm not sure this is the correct translation for the word)... I don't know if there is an explanation here, you just have to take it as it is... Kindda like the weight of a kilo/pound or the volume of a liter...

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Ian Stewart: GMAT Instructor; Posts: 2623; Joined: Mon Jun 02, 2008 3:17 amFollowed by: 355 members; Location: Montreal; Thanked: 1090 times; GMAT Score:780

by Ian Stewart » Sun Jan 18, 2009 9:03 am

DanaJ wrote:0! = 1 because some guys interested in math thought they should just have that rule a long time ago (we call it a convention in RO, but I'm not sure this is the correct translation for the word)... I don't know if there is an explanation here, you just have to take it as it is... Kindda like the weight of a kilo/pound or the volume of a liter...

You can think of the relation 0! = 1 as a mathematical convention (and yes, convention is the word mathematicians use to describe something that's held true simply by common agreement - e.g. the fact that 1 is not prime is essentially a convention, though a handful of 'eccentric' mathematicians think it ought to be granted prime status). Still, there are good reasons why 0! should equal 1. For example, if you want to work out, using the formula, what 7C7 is equal to, you get:

7!
7! 0!

and since this should be equal to 1 (there's only one set of 7 you can choose from a group of 7), then 0! must be equal to 1.

For online GMAT math tutoring, or to buy my higher-level Quant books and problem sets, contact me at ianstewartgmat at gmail.com

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4meonly: Legendary Member; Posts: 891; Joined: Sat Aug 16, 2008 4:21 amFollowed by: 1 member; Thanked: 27 times; GMAT Score:660(

by 4meonly » Sun Jan 18, 2009 9:04 am

OK, I will consider them to be axioms (fundamental truth).
But I am still curious))

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Ian Stewart: GMAT Instructor; Posts: 2623; Joined: Mon Jun 02, 2008 3:17 amFollowed by: 355 members; Location: Montreal; Thanked: 1090 times; GMAT Score:780

by Ian Stewart » Sun Jan 18, 2009 9:05 am

And 0^0 (which you'll never need to worry about on the GMAT) is undefined, because, if you think about what it 'should' be equal to, you arrive at different answers. If k is not zero, 0^k = 0 for all numbers k, while k^0 = 1 for all numbers k. So should 0^0 = 0, or should it be 1?

In some applications, 0^0 is accepted to be equal to 1, but for GMAT purposes, it's not defined. I've never seen a question where you'd need to know that, however.

For online GMAT math tutoring, or to buy my higher-level Quant books and problem sets, contact me at ianstewartgmat at gmail.com

ianstewartgmat.com

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4meonly: Legendary Member; Posts: 891; Joined: Sat Aug 16, 2008 4:21 amFollowed by: 1 member; Thanked: 27 times; GMAT Score:660(

by 4meonly » Sun Jan 18, 2009 9:17 am

Again GMAT Club

What is the value of integer J ?
(1) |J| = J^(-1)
(2) J^J=1

From S1 we have that J=1. Sufficient.
From S2 we also learn that J is 1; 0^0 is a non-existent value.
The correct answer is D.

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satish.nagdev: Master | Next Rank: 500 Posts; Posts: 130; Joined: Sat Dec 29, 2007 5:35 am; Location: SGP; Thanked: 5 times

0!

by satish.nagdev » Wed Jan 21, 2009 7:48 am

Hi,
I was just curious to know more about 0! bit, the link made sense to me

here is what i found https://mathforum.org/library/drmath/view/57128.html

mathematically it makes sense there will be infinite numbers (real) between 0 and 1 and we can't keep multiplying those to get 1

sorry if it doesn't make sense

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