Author 
Message 
TAGS:

Hide Tags

Experts' Global Representative
Joined: 19 Feb 2010
Posts: 235

0 Raised to 0  Infinite versus NonDefined
[#permalink]
Show Tags
23 Mar 2018, 09:37
Hello, I found the following question in a different thread and felt it would be nice to start a new thread on this as 'infinite' and 'nondefined' are often considered the same while Mathematically, they are different. Here we go... ichadaram wrote: According to Gmat what is the value of 0 raised to 0???? First thing first: This will not show up on GMAT. However, for the numbers lovers here... 0^0 is 'not defined'. Please understand the following: 1). 0^0 is not 1. 2). 0^0 is not 0. 3). 0^0 is not 'infinite'. While we use the terms 'infinite' and 'not defined' interchangeably, there is a significant difference.Let me try to explain: 'Infinite' is a number larger than all finite (or countable) numbers. Examples: 1/0, 2/0 etc. 'Non defined' suggests that a unique, defined answer is not possible. Examples: 0/0 (0 divided by anything is 0 but anything divided by 0 is infinite; hence, 'nondefined'). 0^0 (0 raised to power anything is 0 but anything raised to power 0 is 1; hence, 'nondefined'). All the best! Maxximus
_________________



Intern
Joined: 02 Mar 2016
Posts: 18
Concentration: Technology, General Management

Re: 0 Raised to 0  Infinite versus NonDefined
[#permalink]
Show Tags
21 May 2019, 05:58
Maxximus wrote: Hello, I found the following question in a different thread and felt it would be nice to start a new thread on this as 'infinite' and 'nondefined' are often considered the same while Mathematically, they are different. Here we go... ichadaram wrote: According to Gmat what is the value of 0 raised to 0???? First thing first: This will not show up on GMAT. However, for the numbers lovers here... 0^0 is 'not defined'. Please understand the following: 1). 0^0 is not 1. 2). 0^0 is not 0. 3). 0^0 is not 'infinite'. While we use the terms 'infinite' and 'not defined' interchangeably, there is a significant difference.Let me try to explain: 'Infinite' is a number larger than all finite (or countable) numbers. Examples: 1/0, 2/0 etc. 'Non defined' suggests that a unique, defined answer is not possible. Examples: 0/0 (0 divided by anything is 0 but anything divided by 0 is infinite; hence, 'nondefined'). 0^0 (0 raised to power anything is 0 but anything raised to power 0 is 1; hence, 'nondefined'). All the best! Maxximus can you please throw some light on the following questions? 1.Is 0 a multiple of all numbers? (My answer: Yes) 2. Are all numbers multiple of 0? (my answer: No) 3. Is 0 a factor of all numbers? (my answer: No) 4. Are all numbers factors of 0? (my answer: Yes)



Math Expert
Joined: 02 Sep 2009
Posts: 59269

0 Raised to 0  Infinite versus NonDefined
[#permalink]
Show Tags
21 May 2019, 06:13
NA_JS wrote: Maxximus wrote: Hello, I found the following question in a different thread and felt it would be nice to start a new thread on this as 'infinite' and 'nondefined' are often considered the same while Mathematically, they are different. Here we go... ichadaram wrote: According to Gmat what is the value of 0 raised to 0???? First thing first: This will not show up on GMAT. However, for the numbers lovers here... 0^0 is 'not defined'. Please understand the following: 1). 0^0 is not 1. 2). 0^0 is not 0. 3). 0^0 is not 'infinite'. While we use the terms 'infinite' and 'not defined' interchangeably, there is a significant difference.Let me try to explain: 'Infinite' is a number larger than all finite (or countable) numbers. Examples: 1/0, 2/0 etc. 'Non defined' suggests that a unique, defined answer is not possible. Examples: 0/0 (0 divided by anything is 0 but anything divided by 0 is infinite; hence, 'nondefined'). 0^0 (0 raised to power anything is 0 but anything raised to power 0 is 1; hence, 'nondefined'). All the best! Maxximus can you please throw some light on the following questions? 1.Is 0 a multiple of all numbers? (My answer: Yes) 2. Are all numbers multiple of 0? (my answer: No) 3. Is 0 a factor of all numbers? (my answer: No) 4. Are all numbers factors of 0? (my answer: Yes) 1. Yes. 2. No. 0 is not a divisor of any number. 3. 0 is not a factor of any number. 4. Yes. 0 is divisible by every number, except 0 itself. ZERO. 1. 0 is an integer. 2. 0 is an even integer. An even number is an integer that is "evenly divisible" by 2, i.e., divisible by 2 without a remainder and as zero is evenly divisible by 2 then it must be even. 3. 0 is neither positive nor negative integer (the only one of this kind). 4. 0 is divisible by EVERY integer except 0 itself. 5. \(0^0\), in some sources equals to 1, some mathematicians say it's undefined. Anyway you won't need this for GMAT. "During the past decade, mathematicians argued extensively about the value of 0^0. Some answer that 0^0 = 1, while others answer that 0^0 is undefined. In the unlikely event that this question appears in some format or is a required intermediary calculation, the correct answer is more likely that 0^0 = 1." http://www.platinumgmat.com/gmat_study_ ... ial_powersand: "Note: the case of 0^0 is not tested on the GMAT." http://www.manhattangmat.com/npexponents.cfmCheck for more below threads: ALL YOU NEED FOR QUANT ! ! !Ultimate GMAT Quantitative MegathreadHope it helps.
_________________



Intern
Joined: 02 Mar 2016
Posts: 18
Concentration: Technology, General Management

Re: 0 Raised to 0  Infinite versus NonDefined
[#permalink]
Show Tags
21 May 2019, 06:26
Thanks, it helped. I do not find any methof to prove 0^0 as 1 (however I can prove 0^0 as undefined assuming 0 divided by 0 is undefined)  anyway as you suggests and I take it as a word of caution that this won't appear in GMAT so I need not to worry. Cool



Experts' Global Representative
Joined: 19 Feb 2010
Posts: 235

Re: 0 Raised to 0  Infinite versus NonDefined
[#permalink]
Show Tags
25 May 2019, 08:51
Sorry, just noticed this post. Thanks Bunuel, for answering this on my behalf. Kudos! Bunuel wrote: NA_JS wrote: Maxximus wrote: Hello,
I found the following question in a different thread and felt it would be nice to start a new thread on this as 'infinite' and 'nondefined' are often considered the same while Mathematically, they are different.
Here we go...
According to Gmat what is the value of 0 raised to 0????
First thing first: This will not show up on GMAT.
However, for the numbers lovers here...
0^0 is 'not defined'.
Please understand the following:
1). 0^0 is not 1.
2). 0^0 is not 0.
3). 0^0 is not 'infinite'.
While we use the terms 'infinite' and 'not defined' interchangeably, there is a significant difference.
Let me try to explain:
'Infinite' is a number larger than all finite (or countable) numbers. Examples: 1/0, 2/0 etc.
'Non defined' suggests that a unique, defined answer is not possible. Examples: 0/0 (0 divided by anything is 0 but anything divided by 0 is infinite; hence, 'nondefined'). 0^0 (0 raised to power anything is 0 but anything raised to power 0 is 1; hence, 'nondefined').
All the best! Maxximus can you please throw some light on the following questions? 1.Is 0 a multiple of all numbers? (My answer: Yes) 2. Are all numbers multiple of 0? (my answer: No) 3. Is 0 a factor of all numbers? (my answer: No) 4. Are all numbers factors of 0? (my answer: Yes) 1. Yes. 2. No. 0 is not a divisor of any number. 3. 0 is not a factor of any number. 4. Yes. 0 is divisible by every number, except 0 itself. ZERO. 1. 0 is an integer. 2. 0 is an even integer. An even number is an integer that is "evenly divisible" by 2, i.e., divisible by 2 without a remainder and as zero is evenly divisible by 2 then it must be even. 3. 0 is neither positive nor negative integer (the only one of this kind). 4. 0 is divisible by EVERY integer except 0 itself. 5. \(0^0\), in some sources equals to 1, some mathematicians say it's undefined. Anyway you won't need this for GMAT. "During the past decade, mathematicians argued extensively about the value of 0^0. Some answer that 0^0 = 1, while others answer that 0^0 is undefined. In the unlikely event that this question appears in some format or is a required intermediary calculation, the correct answer is more likely that 0^0 = 1." http://www.platinumgmat.com/gmat_study_ ... ial_powersand: "Note: the case of 0^0 is not tested on the GMAT." http://www.manhattangmat.com/npexponents.cfmCheck for more below threads: ALL YOU NEED FOR QUANT ! ! !Ultimate GMAT Quantitative MegathreadHope it helps.
_________________



Experts' Global Representative
Joined: 19 Feb 2010
Posts: 235

Re: 0 Raised to 0  Infinite versus NonDefined
[#permalink]
Show Tags
25 May 2019, 08:54
NA_JS wrote: Thanks, it helped. I do not find any methof to prove 0^0 as 1 (however I can prove 0^0 as undefined assuming 0 divided by 0 is undefined)  anyway as you suggests and I take it as a word of caution that this won't appear in GMAT so I need not to worry. Cool Yes, logically 0^0 is not defined. Once again, the reasoning is 'Non defined' suggests that a unique, defined answer is not possible. Examples: 0/0 (0 divided by anything is 0 but anything divided by 0 is infinite; hence, 'nondefined'). 0^0 (0 raised to power anything is 0 but anything raised to power 0 is 1; hence, 'nondefined'). Nonetheless, as Bunuel mentioned, this won't appear on GMAT. All the best! Experts' Global
_________________



GMAT Tutor
Joined: 24 Jun 2008
Posts: 1827

Re: 0 Raised to 0  Infinite versus NonDefined
[#permalink]
Show Tags
25 May 2019, 10:19
Maxximus wrote: 'Infinite' is a number larger than all finite (or countable) numbers. Examples: 1/0, 2/0 etc.
This is not correct. 1/0 and 2/0 are undefined, just as 0^0 is undefined. 1/0 and 2/0 are not "infinite". Any mathematical reference at all will confirm this. One way to see why this is the case: for 0^0, say, if we take the expression 0^x, where x is positive, we know 0^x = 0. So if we imagine making x infinitely close to 0, 0^x should be 0. But if we do the same for x^0, the answer should be 1. There's no way to decide whether 0^0 should be 0 or 1, so it is undefined. The same is true for 1/x. If we imagine x getting infinitely close to 0, from above, i.e. when x is positive, 1/x gets larger and larger. But if we imagine x approaching zero from below (so x is negative), 1/x gets smaller and smaller. So it does not make sense to say 1/0 is "infinite", since it makes as much sense to say it is "negatively infinite". These are really calculus questions, so they're out of the scope of the GMAT, but for GMAT purposes, test takers should consider x/0 to be undefined (or in other words "mathematically nonsensical"). Everything Bunuel says above about 0 is correct, though the external link he cites about 0^0 is not correct; that expression is undefined on the GMAT, and there will absolutely never be a circumstance where it "appears in some format or is a required intermediary calculation".
_________________
GMAT Tutor in Toronto
If you are looking for online GMAT math tutoring, or if you are interested in buying my advanced Quant books and problem sets, please contact me at ianstewartgmat at gmail.com



Intern
Joined: 02 Mar 2016
Posts: 18
Concentration: Technology, General Management

Re: 0 Raised to 0  Infinite versus NonDefined
[#permalink]
Show Tags
26 May 2019, 05:50
Maxximus wrote: NA_JS wrote: Thanks, it helped. I do not find any methof to prove 0^0 as 1 (however I can prove 0^0 as undefined assuming 0 divided by 0 is undefined)  anyway as you suggests and I take it as a word of caution that this won't appear in GMAT so I need not to worry. Cool Yes, logically 0^0 is not defined. Once again, the reasoning is 'Non defined' suggests that a unique, defined answer is not possible. Examples: 0/0 (0 divided by anything is 0 but anything divided by 0 is infinite; hence, 'nondefined'). 0^0 (0 raised to power anything is 0 but anything raised to power 0 is 1; hence, 'nondefined'). Nonetheless, as Bunuel mentioned, this won't appear on GMAT. All the best! Experts' GlobalNicely put. However, if I am gonna prove 0^0 as undefined via equations it would be as following: 0^0 = 0^(11) {11=0; hence putting 0 as 11} 0^(11) = (0^1 * 0^1) = (0^1/0^1) (using power operations) hence 0^0 = 0/0 and which is undefined. Again, not relevant to GMAT




Re: 0 Raised to 0  Infinite versus NonDefined
[#permalink]
26 May 2019, 05:50






