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Featured Definitions but debates?

Discussion in 'Science and Religion' started by YoursTrue, Apr 28, 2021.

  1. YoursTrue

    YoursTrue We know gravity by happenstance. (Newton)

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    Of course, this is about debates. But -- for me -- it's hard to debate the following: Thoughts are appreciated, though.

    "Does Infinity have a beginning? It really just depends on the infinity you describe, whether it will have a beginning or not. Most infinities do have beginnings, simply because in order to tangibly grasp the concept of whatever infinity we are talking about (just based on the limitations of the human mind) we generally need a starting point." What Is The Largest Number Before Infinity? - The Biggest (the-biggest.net)
     
  2. Left Coast

    Left Coast Circular File Complaint Analyst
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    Infinity is a quantity, so the question is a bit oddly phrased. It's like asking if 2 has a beginning.
     
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  3. Left Coast

    Left Coast Circular File Complaint Analyst
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    We should ask the resident math professor though. @Polymath257!!
     
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  4. Twilight Hue

    Twilight Hue Twilight, not bright nor dark, good nor bad.

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    It's just as impossible to think of infinity as having boundaries as much as it's impossible to think everything has to have a beginning.
     
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  5. Shadow Wolf

    Shadow Wolf Rival's Wife

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    Something like the value of pi goes on forever, or infinity. We can say the 10th digit back is 6 (rounding up), but we can't express the actual fact pi goes on forever. The best we can do is the "...," to signify the value stated is an approximation.
    So "what is the number before infinity" doesn't really have an answer, as infinity in its abstract existence may or may not have a beginning, but it cannot have an end. Having an end disqualifies it from being infinity, as it fails to continue indefinitely.
     
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  6. ecco

    ecco Veteran Member

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    If Infinity is a quantity, then are the following mathematically correct or just meaningless?
    Infinity + Infinity = Infinity
    Infinity x Infinity = Infinity
    Infinity^Infinity = Infinity



    Infinity is more of an abstract idea than an actual quantity.
     
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  7. RestlessSoul

    RestlessSoul Well-Known Member

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    Infinity has neither a beginning nor an end. That’s the whole point, surely? A thing without limits has no boundaries

    And if it exists at all, it can only exist beyond time and space.
     
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  8. Left Coast

    Left Coast Circular File Complaint Analyst
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    I believe they're correct...right Teach? @Polymath257

    It is definitely an abstract idea, but it denotes an amount of something...just an endless amount (duration, speed, number of widgets, etc.).
     
  9. YoursTrue

    YoursTrue We know gravity by happenstance. (Newton)

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    Infinity is a quantity? You can count infinity?
     
  10. YoursTrue

    YoursTrue We know gravity by happenstance. (Newton)

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    Can you tell that to Left Coast please?
     
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  11. Polymath257

    Polymath257 Think & Care
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    There are several different notions of infinity.

    Infinity as a limit describes what happens to a function, and simply describes some variable getting larger and larger as some other variable does something.

    Infinity as a quantity (known as cardinality) is a different notion of infinity. But, there are different sizes of such infinite quantities. The smallest such infinity is that of the 'number' of counting numbers (positive integers). The 'number' of decimal numbers is a larger infinity than this.

    There are also ordinal concepts of infinity. Such can have either infinite ascent, infinite descent, or both.

    There is no 'largest number', and no 'largest number before infinity'. And infinite sets need not have a 'start' nor an 'end'.

    What happens here depends on the type of infinity. For limits, these equations are all correct.

    For cardinals, a sum or product of infinite cardinals is the larger of the two. Exponentiation is a lot trickier. If you want an exposition, I will be happy to give one after I'm back from vacation.

    For ordinal infinities, things get stranger.

    Boundaries are a concept from geometry (or topology). Most versions of infinity are not in that context, so the notion simply doesn't apply.

    Infinite in extent is different than having no boundary. For example, the surface of a sphere has no boundary, but is finite.
     
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  12. Left Coast

    Left Coast Circular File Complaint Analyst
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    No, you can't, because obviously infinite series do not end. You can start, but you'd never finish. My point was that the question "does infinity have a beginning?" does not really make sense.
     
  13. Polymath257

    Polymath257 Think & Care
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    Yes, for cardinal infinities.
     
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  14. shunyadragon

    shunyadragon shunyadragon
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    By definition from any point in our physical existence or time infinity does not have an end.
     
  15. Heyo

    Heyo Well-Known Member

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    Take the natural numbers. They have a beginning at 1 (0) but no end. (I.e. there is a smallest number (a beginning) but not greatest number (no end)).

    [​IMG]
     
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  16. Twilight Hue

    Twilight Hue Twilight, not bright nor dark, good nor bad.

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    How can it not exist? Infinity must be a reality.
     
  17. Twilight Hue

    Twilight Hue Twilight, not bright nor dark, good nor bad.

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    I like that concept of finite and infinity, and it certainly put things in perspective, but it gets too linear and begs a new question of how about any direction above the surface of the sphere?

    For me you cannot escape infinity because any boundary can be prone to circumnavigation that a boundary itself is subject to infinity.
     
  18. Polymath257

    Polymath257 Think & Care
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    Take the negatives of the natural numbers. They have an end (0 or -1) but no beginning. Take *all* integers. They have neither a beginning nor an end.
     
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  19. Polymath257

    Polymath257 Think & Care
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    First, pi is a nice, finite number. It is a bit more than 3 and certainly is less than 4.

    You are talking about a *decimal* expansion of the number pi. And, yes, that decimal expansion is infinite. And, yes, we most certainly *can* express that this expansion is infinite. We know that pi is irrational and all irrational numbers have an infinite decimal expansion. But, then, so does 1/3.

    If you look at the negative integers, that is an infinite set that has an end (a maximum) but no beginning.
    \
    All that it means to be infinite is that it is not finite. In other words, it cannot be put into a one to one correspondence with some natural number. Some infinite sets have an 'end', (a maximum), some have a beginning (a minimum), some have both, and some have neither.

    For example, the collection of all fractions strictly between 0 and 1 has no initial and no final member. if you include both 0 and 1, then it has both while still being infinite.
     
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  20. Shadow Wolf

    Shadow Wolf Rival's Wife

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    We can't express it in a numeric value like we can 5 or 60. It can only be visually represented in written form as an approximation that acknowledges it extends on. Just as your example with fractions. We can't visually express that in any accurate way that includes all numbers, so you give a couple of sentences to express this idea.
     
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