Dpends on whether you use the real definition, or the newfangled one. If it's no factors other than one and itself, it's one. If you prefer the abomination "exactly two distinct factors", it's 2.
Actually Darren, that's not quite true. The new definition is now accepted as true, but back in my school days the other was accepted and taught. I had never heard of the new definition until I started teaching. And, as one whose first love is not math, the older one is much less awkward verbally, and adds very little. Yes, you can write 6 as 2x3 or 1x2x3, or 1x1x2x3, but why would you? It would be just as easy to ask for the simplest prime factorization, and leave 1 prime. I accept the distinction, but I don't have to ike it. Check Wikepedia, prime numbers, primality of one.
I would argue that even if you use the definition "one and itself" the AND implies there must be two factors. You probably wouldn't be okay with someone saying they are going to no stores, other than Target and Target. Using "and" implies a second, different item. Therefore 1 does not fit that definition of a prime number.
A legit interpretation, which nonetheless doesn't change the fact that when that definition was used,one was considered prime. Just another example of lies I was taught in math class, like, "you can't have less than zero" or you can't take the square root of a negative number" or "some quadratic equations have no solutions"
I tell even my low-level algebra students that if the discriminant of a quadaratic equation is negative that there's no *real* answer. I also say that *in Algebra 1* we don't take the square root of a negative number.
Didn't suggest you did . . . the lies come largely from our less mathemetically trained compatriots in the lower levels.. .that's where my experience came from.
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ReplyDelete-Mark Roulo
The smallest prime is 2. 1 is not prime because of the Fundamental Theorem of Arithmetic. (Look it up.)
ReplyDeleteYou know I stink at math: 2?
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ReplyDeleteDpends on whether you use the real definition, or the newfangled one. If it's no factors other than one and itself, it's one. If you prefer the abomination "exactly two distinct factors", it's 2.
ReplyDeleteThere's only one correct definition, max.
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ReplyDeleteThe smallest prime is 2.
ReplyDeleteActually Darren, that's not quite true. The new definition is now accepted as true, but back in my school days the other was accepted and taught. I had never heard of the new definition until I started teaching. And, as one whose first love is not math, the older one is much less awkward verbally, and adds very little. Yes, you can write 6 as 2x3 or 1x2x3, or 1x1x2x3, but why would you? It would be just as easy to ask for the simplest prime factorization, and leave 1 prime.
ReplyDeleteI accept the distinction, but I don't have to ike it. Check Wikepedia, prime numbers, primality of one.
I would argue that even if you use the definition "one and itself" the AND implies there must be two factors. You probably wouldn't be okay with someone saying they are going to no stores, other than Target and Target. Using "and" implies a second, different item. Therefore 1 does not fit that definition of a prime number.
ReplyDeleteA legit interpretation, which nonetheless doesn't change the fact that when that definition was used,one was considered prime. Just another example of lies I was taught in math class, like, "you can't have less than zero" or you can't take the square root of a negative number" or "some quadratic equations have no solutions"
ReplyDeleteI tell even my low-level algebra students that if the discriminant of a quadaratic equation is negative that there's no *real* answer. I also say that *in Algebra 1* we don't take the square root of a negative number.
ReplyDeleteI don't lie to my students.
Didn't suggest you did . . . the lies come largely from our less mathemetically trained compatriots in the lower levels.. .that's where my experience came from.
ReplyDelete