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: 7,618 Thanks: 2608 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: 20,373 Thanks: 2010 
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: 20,373 Thanks: 2010 
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: 20,373 Thanks: 2010 
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 <and> 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: 20,373 Thanks: 2010 
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 <and> 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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