Download ArticleDownload ArticleThis article was reviewed by Grace Imson, MA and by How.com.vn staff writer, Johnathan Fuentes. Grace Imson is a math teacher with over 40 years of teaching experience. Grace is currently a math instructor at the City College of San Francisco and was previously in the Math Department at Saint Louis University. She has taught math at the elementary, middle, high school, and college levels. She has an MA in Education, specializing in Administration and Supervision from Saint Louis University.
This article has been fact-checked, ensuring the accuracy of any cited facts and confirming the authority of its sources.
This article has been viewed 65,444 times.
If you’re taking a math class, you’ll definitely encounter integers, as well as positive and negative numbers. But where does 0 fall within these categories? Is it positive or negative? Is it an integer or not? If these questions have you scratching your head, you’re not alone. 0 is an oddball in math, and categorizing it requires some extra thinking and creativity. This guide will help you understand exactly how 0 fits in with respect to positive and negative integers. Keep reading for a crystal clear explanation, plus a few examples to really bring these ideas home.
Things You Should Know
- Zero is an integer, but it’s neither positive nor negative. It’s the only number that’s not positive or negative.
- Zero is neither greater than zero nor less than zero. Therefore, by this definition, it’s neither positive nor negative.
- Zero is still an integer because it’s a whole number and doesn’t contain any fractional part. This means it contains no fractions or decimals.
- A positive integer is a whole number greater than zero, while a negative integer is a whole number less than zero.
Steps
Proof that Zero Can’t be Positive or Negative
Download Article
If 0 was positive, it would break the rules of multiplying negative numbers. Let’s use the example -2 x 0 = 0, assuming zero is positive. We know that -2 is a negative number. We also know that if we multiply a negative number by a positive number, the answer will always be negative.[3] Therefore, if we assume 0 is positive, then -2 x 0 should give us a negative answer. But the answer is 0, which we said was positive. This is a contradiction, which means our original assumption was incorrect.[4]- Since a number can’t be positive and negative at the same time, we must assume that 0 is neither positive nor negative.
If 0 was negative, it’d also break the rules of multiplying negative numbers. Let’s try -2 x 0 = 0 again, assuming zero is negative this time. We know that -2 is a negative number. We also know that if we multiply a negative number by another negative number, the answer will always be positive.[5] Therefore, if we assume 0 is negative, then -2 x 0 should give us a positive answer. But the answer is 0, which we assumed was negative. Once again, we have a contradiction. This proves that our original assumption was wrong.[6]- A number can’t be negative and positive at the same time. Therefore, 0 is neither positive nor negative.
Community Q&A
- QuestionWhy is 0 times x equals to 0?
Community AnswerThe reason this is true is that, according to the "zero property of multiplication," anything multiplied by zero equals zero. - QuestionWhy can't 0 be both positive and negative?
Community AnswerIn one sense, that is a meaningless and inconceivable condition. In another sense, however, it could be considered true: zero is "more positive" than negative numbers and at the same time "more negative" than positive numbers. (This is a rather trivial notion, however, in that something similar could be said of any number.) - QuestionWhat is the absolute value of negative zero?
I_l1ke_gam3sCommunity AnswerThere is no such thing as “negative zero”. Zero is neither positive nor negative. Zero is just zero, with an absolute value of zero.
Tips
References
- ↑ https://mathworld.wolfram.com/Zero.html
- ↑ https://www.usf.edu/intousf/documents/math_vocabulary_and_common_symbols.pdf
- ↑ https://web.gccaz.edu/~johwd63181/MAT115/chapter1/text/Section%201.3.pdf
- ↑ https://www.ma.imperial.ac.uk/~buzzard/maths/teaching/18Aut/M1F/solns03.pdf
- ↑ https://web.gccaz.edu/~johwd63181/MAT115/chapter1/text/Section%201.3.pdf
- ↑ https://www.ma.imperial.ac.uk/~buzzard/maths/teaching/18Aut/M1F/solns03.pdf
About This Article
Did this article help you?
⚠️ Disclaimer:
Content from Wiki How English language website. Text is available under the Creative Commons Attribution-Share Alike License; additional terms may apply.
Wiki How does not encourage the violation of any laws, and cannot be responsible for any violations of such laws, should you link to this domain, or use, reproduce, or republish the information contained herein.
- - A few of these subjects are frequently censored by educational, governmental, corporate, parental and other filtering schemes.
- - Some articles may contain names, images, artworks or descriptions of events that some cultures restrict access to
- - Please note: Wiki How does not give you opinion about the law, or advice about medical. If you need specific advice (for example, medical, legal, financial or risk management), please seek a professional who is licensed or knowledgeable in that area.
- - Readers should not judge the importance of topics based on their coverage on Wiki How, nor think a topic is important just because it is the subject of a Wiki article.
