My Math Forum new type of number

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 February 9th, 2019, 02:53 AM #1 Banned Camp   Joined: Feb 2019 From: Casablanca Posts: 23 Thanks: 2 new type of number Hello everyone, In admit the existence of a negative square thus the existence of i, and that X <= Y and Y> = X without X = Y For the numbers on real. So Let the number X such that X <1 and X> 1 with X # 1 And the number Z such that Z <-1 and Z> -1 with Z # -1 The two numbers X and Z are found in the real set with this definition as the case of the number i. Do X and Z exist as i? What can we say about X and Z?
 February 9th, 2019, 03:14 AM #2 Math Team   Joined: Dec 2013 From: Colombia Posts: 7,675 Thanks: 2655 Math Focus: Mainly analysis and algebra We can say they definitely aren't in the reals. What's this new operation $#$?
 February 9th, 2019, 04:06 AM #3 Global Moderator   Joined: Dec 2006 Posts: 20,939 Thanks: 2210 For reals x and y, x $\small\leqslant$ y and y $\small\geqslant$ x have precisely the same meaning: either x < y or x = y. For numbers that are imaginary, not real, greater than and less than are undefined.
 February 9th, 2019, 04:07 AM #4 Banned Camp   Joined: Feb 2019 From: Casablanca Posts: 23 Thanks: 2 X # 1 means X is different from 1
 February 9th, 2019, 04:14 AM #5 Global Moderator   Joined: Dec 2006 Posts: 20,939 Thanks: 2210 It's impossible for any real to be both less than 1 and greater than 1 simultaneously. It's impossible for any real to be both less than -1 and greater than -1 simultaneously.
 February 9th, 2019, 04:26 AM #6 Banned Camp   Joined: Feb 2019 From: Casablanca Posts: 23 Thanks: 2 X and Z are not real or complex numbers. it's a new type of number.
 February 9th, 2019, 04:54 AM #7 Global Moderator   Joined: Dec 2006 Posts: 20,939 Thanks: 2210 In that case, it doesn't make sense to say "X and Z are found in the real set".
 February 9th, 2019, 05:16 AM #8 Banned Camp   Joined: Feb 2019 From: Casablanca Posts: 23 Thanks: 2 The definition of X and Z show that X and Z do not belong to R, and the use of shows that X and Z do not belong to C either. Therefore the numbers X and Z are not real or complex. Last edited by skipjack; February 9th, 2019 at 01:07 PM.
 February 9th, 2019, 06:46 AM #9 Global Moderator   Joined: Dec 2006 Posts: 20,939 Thanks: 2210 Can you clarify the definition, as it isn't clear enough for me to understand it? Whatever definition you use, it doesn't make sense to say X and Z are found in the real set if they're not real.
 February 9th, 2019, 06:57 AM #10 Banned Camp   Joined: Feb 2019 From: Casablanca Posts: 23 Thanks: 2 My definition is simple X is greater and less than 1 without being equal to 1. So X do not belong to R, and since I used to define it, it does not belong to C either. Last edited by skipjack; February 9th, 2019 at 01:11 PM.

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