Pronunciation: /dɪˈs tɪŋkt/ ?

Two or more math objects are distinct if they are not the same.[1] Mathematicians use the word distinct to emphasize that two or more math objects are not identical.

For example, a quadratic equation may have two distinct complex roots, two distinct real roots or two real roots that are the same.

x^2-x-6=0 implies (x+2)(x-3)=0, x has 2 distinct real roots. x^2+2x+2=0 implies (x+1)(x+1)=0, x does not have 2 distinct roots. x^2+4=0 implies (x+2i)(x-2i) = 0, x has 2 distinct complex roots.

Another example is the use of distinct prime factors. The number 12 has a prime factorization of 2^2*3, whereas its distinct prime factors are 2,3.

To prove two objects are distinct, it helps to find some property of the two numbers that is different. For example, if x has two roots, 2 and 3, one could note that one of the value is even and the other is odd. This may seem silly in its simpleness, but in advanced math it is often useful.


  1. distinct. http://wordnet.princeton.edu/. WordNet. Princeton University. (Accessed: 2011-01-08). http://wordnetweb.princeton.edu/perl/webwn?s=distinct&sub=Search+WordNet&o2=&o0=1&o7=&o5=&o1=1&o6=&o4=&o3=&h=.

Cite this article as:

Distinct. 2010-01-23. All Math Words Encyclopedia. Life is a Story Problem LLC. http://www.allmathwords.org/en/d/distinct.html.


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2008-12-13: Initial version (McAdams, David.)

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