Use the definition of less than to show each of the following:
a. 2 < 4
b. 3 < 100
c. 0 < 3
I would show on a number line that the less than number is always to the left of the other number.
To show each of the following using the definition of less than:
a. 2 < 4:
The definition of less than states that a < b if b - a is a positive number. In this case, we subtract 2 from 4:
4 - 2 = 2
Since the result is a positive number (2), we can conclude that 2 is less than 4. Therefore, 2 < 4 is true.
b. 3 < 100:
Similarly, we can apply the definition of less than by subtracting 3 from 100:
100 - 3 = 97
Since the result (97) is positive, we can conclude that 3 is less than 100. Therefore, 3 < 100 is true.
c. 0 < 3:
In this case, we subtract 0 from 3:
3 - 0 = 3
Since the result is positive (3), we can conclude that 0 is less than 3. Hence, 0 < 3 is true.