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InfinityInfinity is always more than 0 and less than 1! |

Why |

Because, anything greater than 1 is combination of 1s. Thanks |

Are you high? |

*Ba-dum tish* |

I'm a sucker for threads that ponder the infinite, even when they lead to nonsense. I saw this, got interested, clicked on it, and then wow... just wow. You got me. Good one. :p |

Thank you all. Than here is one question for you guys: how many infinities are in between 0 and 1? |

Quote:
If I consider the number of different infinite subsets of rational numbers that can be created from the rationals on the interval (0, 1), then the answer is a cardinal number commonly denoted $2^{\aleph_0}$. |

Thanks again! Well, how should I describe for example: 0.11111... or 0.99999... or 0.12451234512345... Do they belong to "infinity" ? Just curious. Thanks |

Quote:
To clarify this, consider the decimal .1234512345... Now that looks like it encodes an infinite amount of information. But actually it has a repeating block so it's a rational number. In fact it's $\frac{12345}{99999}$. So it only encodes two whole numbers, not infinitely many. A number is an abstract object that may have many different representations. A real number has a decimal representation (sometimes two) but the representation is not the number. It does happen to be the case that decimal representation is flawed. Some numbers have two different representations. Others only encode a finite amount of information, yet their decimal representation is infnite, as we saw with $.1234512345 \dots$ So we shouldn't confuse a finite number with its infinite decimal representation. In fact all real numbers are finite numbers. |

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