Page 83 - Mathematics GRADE 9, DE-STREAMED (MTH1W)

B1.3 Number Sets
use patterns and number relationships to explain density, infinity, and limit as they relate to number sets
Teacher supports
Examples
• patterns and number relationships:
o growing patterns can be extended indefinitely:
• 2,4,6,8,...
• −5,−3,−1,1,...
• 1, 12, 14, 18
• 2,4,8,16,...
• 1,4,9,16,...
• explaining the density of a number set as the probability that a number of a particular type will be
found within a particular set of numbers:
o the set of perfect squares between 0 and 20 is less dense than the set of odd numbers
between 0 and 20 because the respective probabilities are 5 and 10 21 21
o the set of real numbers between −2 and 6 is more dense than the set of integers between −2 and 6 because there is an infinite number of real numbers in that set, but only 7 integers
• exploring the density and infinity of a number set: o using a number line:
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