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Algebra Connections Glossary
identity element for addition  
  0 is the identity element for addition because adding 0 to an expression leaves the expression unchanged.  That is, a + 0 = 0.  (Also see “Additive Identity Property.”)
identity element for multiplication 
  1 is the identity element for multiplication because multiplying an expression by 1 leaves the expression unchanged.  That is, a(1) = a.  (Also see “Multiplicative Identity Property.”)
Identity Property of Addition
  See: Additive Identity Property.
Identity Property of Multiplication   
  See “Multiplicative Identity Property.”
independent variable   
  When one quantity changes in a way that does not depend on the value of another quantity, the value that changes independently is represented with the independent variable.  For example, we might relate the speed of a car to the amount of force you apply to the gas pedal.  Here, the amount of force applied may be whatever the driver chooses, so it represents the independent variable.  The independent variable appears as the input value in an x → y table, and is usually placed relative to the horizontal axis of a graph.  We often use the letter x for the independent variable.  When working with functions or relations, the independent variable represents the input value. (Also see “dependent variable.”)
inductive reasoning   
  Drawing a conclusion based on a pattern.  For example, having seen many multiples of 5 that end in the digit 0 or 5, you might use inductive reasoning to make a hypothesis or conjecture that all multiples of 5 end in the digit 0 or 5.
inequality   
  An inequality consists of two expressions on either side of an inequality symbol.  For example, the inequality 7x + 4.2 < −8 states that the expression 7x + 4.2 has a value less than 8. 
inequality symbols   
  The symbol  ≤  read from left to right means “less than or equal to.”   The symbol  ≥  read from left to right means “greater than or equal to.”  The symbols  <  and  >  mean “less than” and “greater than,” respectively.  For example, “7 < 13” means that 7 is less than 13.
input value   
  The input value is the independent variable in a relation.  We substitute the input value into our rule (equation) to determine the output value.  For example, if we have a rule for how much your phone bill will be if you talk a certain number of minutes, the number of minutes you talk is the input value.  The input value appears first in an x → y table, and is represented by the variable x.  When working with functions, the input value, an element of the domain, is the value put into the function.
integers  
  The set of numbers { . . . −3, −2, −1, 0, 1, 2, 3, . . .  }.
intersection   
  See “point of intersection.”
irrational numbers   
  The set of numbers that cannot be expressed in the form pic, where a and b are integers and b ≠ 0.  For example, π and pic are irrational numbers.
justify   
  To use facts, definitions, rules, and/or previously proven statements in an organized way to convince an audience that a claim (or an answer) is valid or true.  For example, you might justify your claim that x = 2 is a solution to 3x = 6 by pointing out that when you multiply 3 by 2, you get 6. (p. 88)