What is your favorite number?

  • #26
kith
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But it is the clearest way to describe the issue, and I'm sure you can see the intent.
No, I can't see what concerns you. The fundamental theorem of algebra tells us that every polynomial equation has a solution in the complex numbers. If we drop the constraint that our equation needs to be a polynomial equation, it is easy to construct examples which don't have a solution in the complex numbers. For example, [itex]\sin(|z|) = 2[/itex].

I don't see an issue here and I don't understand why you bring up inequalities in response to these statements about equations.

Also this is getting off topic. If you want to discuss it further, you should open a new thread or ask the mentors to fork our discussion from this thread.
 
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  • #28
Ssnow
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##4##
 
  • #29
Tsu
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  • #30
Choppy
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##J = (7^{e - 1/e} - 9) \cdot \pi^{2} ##
 
  • #31
epenguin
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1729 before anyone else claims it!

This is the number (least one that is sum of two cubes writeable in more than one way) in the famous Hardy anecdote about Ramanujan.

I did actually see about 10 years ago a London taxi with registration plate TXI1729.

I bet not a lot of people here have done that. So lifetime acheivement! :approve:
 
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  • #32
tionis
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拾叁
 
  • #33
Svein
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17. There is an old mathematics adage: If you can prove it for x = 17, then it has a good chance to be true for all x.
 
  • #34
EnumaElish
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Pi. It's probably the most or the second most famous irrational number. And it distinctly smells of baked apples and cinnamon.
 
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  • #35
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7.
The smallest of the more 'interesting' primes.
e.g. when I was learning how to express x/y as a decimal, it was 1/7, 2/7, 3/7 etc that made me realise decimals weren't just an uninteresting variation on fractions.
i.e. 0.142857..... , 0.285714.... , 0.428571.... etc
 
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  • #36
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Both 0 and 1 are mentioned as favorite numbers here. It's apparently assumed that by "number" we mostly mean the natural numbers or the non-negative integers. The latter includes 0. However 0 and 1 are neither prime numbers nor composite numbers. They are specifically excluded in the Fundamental Theorem of Arithmetic. Zero and one are algebraic identities. Zero is the additive identity and one is the multiplicative identity. The latter is the reason why 1 can't be prime. It is a "factor" of every natural number. To properly define "prime number" we must exclude 1.

It seems even mathematicians don't know exactly what to do with 0 and 1 in terms of classification. It all seems a bit awkward.
 
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  • #37
bigfooted
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33550336, It was the result of one of my first computer programs!
It convinced me that a connection must exist between perfect numbers and Mersenne primes. You can read all about it on wikipedia now, but it was more difficult to find such information in a small farming village in 1994.
 
  • #38
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I like pi
And e is cool
Favorite is i
 
  • #39
My favourite number... What a curious question.
It is "-1". Why such a -1 be interesting.?
Well, we could set -1 as a very beautiful combination of number e, number i and number phi.
Then, e(i*π) = -1 !!
 
  • #40
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8. Oh, I guess you eight one two
 
  • #41
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Then, e(i*π) = -1 !!
I don't why people like this expression so much, because it has the minus sign in it? I think the most poetic form of Euler's identity is "e^i2π=1" This is a very clean expression, no fussy minus signs, and brings it all around full circle :oldsmile:
 
  • #42
I don't why people like this expression so much, because it has the minus sign in it? I think the most poetic form of Euler's identity is "e^i2π=1" This is a very clean expression, no fussy minus signs, and brings it all around full circle :oldsmile:
Indeed, my e(i*π) = -1 is not the better. Maybe it will be e(i*π) + 1 = 0 since it has number e, i , π, 1 and 0. I wrote e(i*π) = -1 because it simplifies the expression and gives a "-1" which is a number that is not as much as popular as 0. I just wanted to remark that -1 could be a weird and beautiful expresion. I don't know if "e^i2π=1" will be as much as beautiful, since there is a "2" in it, and it is not as important nor beautiful as e, i , π, 1 or 0 (despite that 2 has its own rare properties, like to be the only prime number that is even).
 
  • #43
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I don't know if "e^i2π=1" will be as much as beautiful, since there is a "2" in it, and it is not as important nor beautiful as e, i , π, 1 or 0
I love your passion here, but I still think that my expression is the most beautiful. The fact is that we are stuck with PI and I don't see that changing in the foreseeable future. But a more elegant form of the Euler identity would be to use the Tau term which would eliminate the "2" that you seem to have a problem with. So, it would be e^iτ=1.

 
  • #44
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8. Oh, I guess you eight one two
ROTFLMAO :biggrin: Well done DP.
 

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