The correct answers are as follows:
In high school, I
The correct answers are as follows:
In high school, I vehemently argued with my instructor that there would always be a minute difference between 3.999.... and 4.000... because the 3.9999...... would only ever approach 4.0000 but there still would always be a slight difference.
his answer: If x=3.9999...... then 10x=39.999......
Thus 10x - x = 36.0000 or 9x = 36.000 so x= 4.00000
Note when you subtract the x from 10x that all the .999.... cancel out.
He went on to say that in some higher math models they do not recognize 4.0000 but believe 3.999..... is the more appropriate number. No clue why.
As to 2/3 + 3/4 = 5/7 You go to a baseball double header and your favorite player in the first game goes 2 for 3 and in the second game he goes 3 for 4, thus for the day he went 5 for 7 and his batting avg for the day was .714 as noted in the equation above.
Funny how those remarks made such an impression on me while very little else did in math.
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