Meaning of Greater Than, Less Than Symbols

Date: 11/07/2002 at 09:30:43
From: Neftali Ospino
Subject: Math signs <>

Right now I don't know if <> signs always mean the same or depend on 
the location of the X. For example:

to me 3 < X means all numbers greater than 3
      X < 3 means all numbers less than 3

The sign is the same, but the location of X changes, and so the 
meaning changes. Am I right?

Thanks a lot.

Date: 11/07/2002 at 10:49:04
From: Doctor Ian
Subject: Re: Math signs <>

Hi Neftali,

You're right - the locations of the quantities being compared makes
all the difference. Consider the two sentences:

  The dog bites the man.

  The man bites the dog.

The two sentences have different meanings, but the meaning of 'bite'
stays the same, right? To figure out what's happening, you have to pay 
attention to the locations of the words.    

The same is true for < and >:

  3 < X     The value of 3 is less than the value of X.

  X < 3     The value of X is less than the value of 3.

  3 > X     The value of 3 is greater than the value of X.

  X > 3     The value of X is greater than the value of 3.

The thing on the smaller (i.e., pointy) side of the sign is the
smaller quantity, in much the way that the agent at the beginning of
the sentence is the one doing the biting.

Does this help? 

- Doctor Ian, The Math Forum
  http://mathforum.org/dr.math/