4,320 reputation
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bio website dcproof.com
location Canada
age
visits member for 4 years, 2 months
seen Jan 23 at 16:39

An amateur mathematician, I have developed DC Proof, an educational software program to introduce students to the basic methods of proof. In the style of most mathematics textbooks at the undergraduate level, its simplified rules of logic and set theory are loosely based on standard FOL and ZFC. For more information, a video demo and free download, visit my website. Also visit my math blog.


Jan
21
comment Necessary but not sufficient in logic
I guess I have been out in real world for too long. When I read nonsense like this I try to read between the lines and ascertain the author's intend. A bad habit in some circles. Besides, I qualified my answer, "I this is the case...."
Jan
21
comment Necessary but not sufficient in logic
Then why did the author not state simply: "For hiking on the trail to be safe, it is necessary but not sufficient that berries not be ripe along the trail?"
Jan
20
revised Necessary but not sufficient in logic
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Jan
20
comment Necessary but not sufficient in logic
Thanks Issac. Berries on their own don't present a danger, but they do attract bears. If there no bears in the area, then ripe berries can be tasty snack for hikers. The author, taken literally, is suggesting that ripe berries on their own pose a threat to hikers even if there are no bears in the area.
Jan
20
revised Necessary but not sufficient in logic
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Jan
20
comment Necessary but not sufficient in logic
How about, when there are bears and berries, there is not safety. This doesn't rule out any other dangers on the trail, e.g. thunderstorms.
Jan
20
revised Necessary but not sufficient in logic
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Jan
20
revised Necessary but not sufficient in logic
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Jan
20
revised Necessary but not sufficient in logic
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Jan
20
comment Necessary but not sufficient in logic
The "but not sufficient" is redundant.
Jan
20
comment Necessary but not sufficient in logic
It may help to reword the problem slightly: If grizzly bears have been seen in the area and berries are ripe along the trail, then hiking is not safe along the trail.
Jan
20
revised Necessary but not sufficient in logic
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Jan
19
revised Necessary but not sufficient in logic
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Jan
19
revised Necessary but not sufficient in logic
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Jan
19
answered Necessary but not sufficient in logic
Jan
16
comment Nullary Arithmetic Product (at Wiki)
Depending on your application, you may legitimately want at least two elements in your input list to be multiplied together as you suggest. Or you may want at least one element and return that single value if there is only one element in the list. Or you may return some numerical value (maybe 0 or 1) if the list was empty. Of course, in this case, you could also get a 0 or 1 by multiplying 2 or more elements. It all seems really quite arbitrary -- hardly some universal mathematical truth as seems to be suggested here.
Jan
16
comment Nullary Arithmetic Product (at Wiki)
@BrianM.Scott Thanks for the editing. To use a programming analogy to my 2nd alternative (see edit), if you want to calculate the product of the numerical contents of a variable length array, you might initialize an accumulator variable Prod=1. Then loop through the array multiplying Prod by each element of the array in turn. If the final result was 1, either the array was empty (and no multiplication actually occurred) or every element was equal to 1. What has this got to do with $0^0$?
Jan
15
revised Nullary Arithmetic Product (at Wiki)
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Jan
15
revised Nullary Arithmetic Product (at Wiki)
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Jan
15
revised Nullary Arithmetic Product (at Wiki)
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