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If "point 9 recurring" means the same thing as:
the limit of the sequence 0.9, 0.99, 0.999, etc.
then I know it equals 1 because that's what I was told.
Math in engineering school was like studying hammers. You don't take them apart, and you don't ask why. You just grab one and start hitting things. For five years.
None of the choices above work. The LIMIT of .9999 is 1. Since .9 repeating is not actually the same number as .9 with an infinite number of nines at the end, you're always adding a nine out there to do something with it, right? Sure .9 repeating infinitely is the same as one, but I'd argue that .9 with the repeating symbol is not, since the symbol indicates that the repeating has to take place manually. The repeatin…
it approaches 1 but is not equal to 1.
1/3 = .333333.... 1/3 + 1/3 + 1/3 = 1 So, yes
1/9 = 0.111...
0.111... + 0.111... + ... = 0.999....
9 * 1/9 = 1
1/10 = 0.1
10 * 1/10 = 1According to math folk, yes. According to philosophy folk, no. This crowd is more likely to be math folk. Both crowds just need to get out and relax more.
Why are you interested in getting people's opinions on a matter of fact? "Everyone is entitled to their own opinions, but they are not entitled to their own facts."
Some people regard it as "fact" that the Moon landings were faked. Some people regard it as "fact" that they've been abducted by aliens. Some people regard it as "fact" that they can power their car with water. Some people regard it as "fact" that there is only one size of infinity. Some people regard it as "fact" that you can choose one element from each of infinitely many non-empty sets. Some people regard it as "f…
it approaches 1 but is not equal to 1.
(sorry to see you downvoted - because it is actually sometimes tought to grasp but...) it doesnt approach one- your thinking of a nice graph where the line does approach but never touch, however 0.9... is NOT a function, cannot be plotted. It exists for infinite length. Any distance it is from 1 is constant.
it approaches 1 but is not equal to 1.
(sorry to see you downvoted - because it is actually sometimes tought to grasp but...) it doesnt approach one- your thinking of a nice graph where the line does approach but never touch, however 0.9... is NOT a function, cannot be plotted. It exists for infinite length. Any distance it is from 1 is constant.
the function that writes some number of repeating 9's (replacing the zero in the last decimal place with a 9). This function approaches 1, does it not?
f(1) = 0.9
f(2) = 0.99
f(3) = 0.999
so f as defined above approaches 1
I interpreted the question in the context of numerical precision. Since we are usually not dealing with infinite precision, the two are not equal.
I am familiar with the obvious: 1/3 == 0.3333... and 3 * 1/3 == 1 so 0.9999... == 1
Why are you interested in getting people's opinions on a matter of fact? "Everyone is entitled to their own opinions, but they are not entitled to their own facts."