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- - **new type of number**
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new type of numberHello 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? |

We can say they definitely aren't in the reals. What's this new operation $#$? |

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. |

X # 1 means X is different from 1 |

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. |

X and Z are not real or complex numbers. it's a new type of number. |

In that case, it doesn't make sense to say "X and Z are found in the real set". |

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. |

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. |

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. |

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