Announcement

Collapse

Natural Science 301 Guidelines

This is an open forum area for all members for discussions on all issues of science and origins. This area will and does get volatile at times, but we ask that it be kept to a dull roar, and moderators will intervene to keep the peace if necessary. This means obvious trolling and flaming that becomes a problem will be dealt with, and you might find yourself in the doghouse.

As usual, Tweb rules apply. If you haven't read them now would be a good time.

Forum Rules: Here
See more
See less

Can we discuss this?

Collapse
X
 
  • Filter
  • Time
  • Show
Clear All
new posts

  • Originally posted by lao tzu View Post
    The nth term doesn't approach zero. That's a necessary condition.
    It's a necessary condition for the series to converge, yes.

    My point is that if infinite series is defined for many series though many such series do not reach a convergent limit, then why not so with division?

    Especially as I understand that simple division is not defined as an operation with the divisor being a transcendental number; limits are used to define such divisions. Another way I could pose my question is: why then can't division by a real be defined as an operation across the entire real line, ie including 0, by further extending the division operation to zero? Yes, the result is not a convergent limit, but so are the results of many infinite series.

    Comment


    • Originally posted by Paprika View Post
      It's a necessary condition for the series to converge, yes.

      My point is that if infinite series is defined for many series though many such series do not reach a convergent limit, then why not so with division?
      Divergent series are defined; their values are not. Mut. mut.

      Especially as I understand that simple division is not defined as an operation with the divisor being a transcendental number; limits are used to define such divisions. Another way I could pose my question is: why then can't division by a real be defined as an operation across the entire real line, ie including 0, by further extending the division operation to zero? Yes, the result is not a convergent limit, but so are the results of many infinite series.
      The result of such an extension is, likewise, an expression that can't be evaluated.

      Comment


      • Originally posted by lao tzu View Post
        Divergent series are defined; their values are not. Mut. mut.
        Precisely. So why can't the operation of dividing by zero be defined, with the value of the result being undefined?

        Comment


        • Originally posted by KingsGambit View Post
          Teal's my friend and is a perfectly reasonable thinker, even if I don't agree with her on evolution. She doesn't deserve that.
          Like klaus54 I have no patience with the YEC view of the nature of our physical existence. Upfront and frank Frank. This world view is dangerous nonsense.
          Glendower: I can call spirits from the vasty deep.
          Hotspur: Why, so can I, or so can any man;
          But will they come when you do call for them? Shakespeare’s Henry IV, Part 1, Act III:

          go with the flow the river knows . . .

          Frank

          I do not know, therefore everything is in pencil.

          Comment


          • Originally posted by shunyadragon View Post
            Like klaus54 I have no patience with the YEC view of the nature of our physical existence. Upfront and frank Frank. This world view is dangerous nonsense.
            I'm sure there's a law somewhere that states that if a NatSci thread goes on long enough Shunya will pop in and turn it into a thread about YEC or Cosmology/Bahai.

            Comment


            • Originally posted by Paprika View Post
              So 1/x as x->0 does not converge to a single value.
              1/x as x->0 doesn't converge to any value.

              What about the infinite sum 1-2+3-4+5...?
              It depends on how you define what an infinite sum is, but simple progressive addition doesn't produce any convergence. There are other kinds of ways to define the summing of an infinite number of terms and interestingly they all give 1/4 for the above sum. Euler demonstrated this by defining a new type of infinite sum of terms as the following



              Now for the infinite sum you proposed this type of summation (which the mathematician Abel developed further) gives



              So for some divergent infinite sums its actually possible to find consistent ways of summing them up, and there's a bunch to choose from and various interesting mathematical theorems that revolve around when they work and what it means.

              However the partial sums will be divergent in the above case.

              Comment


              • Originally posted by Leonhard View Post
                1/x as x->0 doesn't converge to any value.
                If we understand x is never equal to the limit. So the value has no bound.
                Last edited by 37818; 02-01-2015, 10:29 AM.
                . . . the gospel of Christ: for it is the power of God unto salvation to every one that believeth; . . . -- Romans 1:16 KJV

                . . . that Christ died for our sins according to the scriptures; And that he was buried, and that he rose again the third day according to the scriptures: . . . -- 1 Corinthians 15:3-4 KJV

                Whosoever believeth that Jesus is the Christ is born of God: . . . -- 1 John 5:1 KJV

                Comment


                • Originally posted by Leonhard View Post
                  I'm sure there's a law somewhere that states that if a NatSci thread goes on long enough Shunya will pop in and turn it into a thread about YEC or Cosmology/Bahai.
                  Simply responding to a previous post. I did not bring the issue up in this thread. Thanks for the airball non-answer.
                  Glendower: I can call spirits from the vasty deep.
                  Hotspur: Why, so can I, or so can any man;
                  But will they come when you do call for them? Shakespeare’s Henry IV, Part 1, Act III:

                  go with the flow the river knows . . .

                  Frank

                  I do not know, therefore everything is in pencil.

                  Comment


                  • Originally posted by 37818 View Post
                    If we understand x is never equal to the limit. So the value has no bound.
                    If x is equal to that limit then you're dividing with zero, which you can't. Its not an aleph_n cardinal number, nor a hyperreal number, nor infinity.

                    Its undefined.

                    Even the limit of 1/x for x->0 is undefined unless its specified from what direction you're approaching 0.

                    Comment


                    • Originally posted by shunyadragon View Post
                      Simply responding to a previous post. I did not bring the issue up in this thread. Thanks for the airball non-answer.
                      Sounds like you could use a break from tweb, you sound kinda aggro.

                      Comment


                      • Originally posted by Leonhard View Post
                        If x is equal to that limit then you're dividing with zero, which you can't. Its not an aleph_n cardinal number, nor a hyperreal number, nor infinity.

                        Its undefined.

                        Even the limit of 1/x for x->0 is undefined unless its specified from what direction you're approaching 0.
                        well my first computer gave infinity as the answer.
                        GE-Analog-1961a.jpg

                        And the default Android calculator also gives infinity as the answer for division by zero.
                        . . . the gospel of Christ: for it is the power of God unto salvation to every one that believeth; . . . -- Romans 1:16 KJV

                        . . . that Christ died for our sins according to the scriptures; And that he was buried, and that he rose again the third day according to the scriptures: . . . -- 1 Corinthians 15:3-4 KJV

                        Whosoever believeth that Jesus is the Christ is born of God: . . . -- 1 John 5:1 KJV

                        Comment


                        • Originally posted by 37818 View Post
                          well my first computer gave infinity as the answer.
                          [ATTACH=CONFIG]3783[/ATTACH]

                          And the default Android calculator also gives infinity as the answer for division by zero.
                          Advanced calculators and modern computers, if they don't outright return a specific error code, should return NaN (Not a Number).
                          Last edited by Leonhard; 02-01-2015, 12:48 PM.

                          Comment


                          • Originally posted by KingsGambit View Post
                            Teal's my friend and is a perfectly reasonable thinker, even if I don't agree with her on evolution. She doesn't deserve that.
                            That's your opinion. I'm sure Cat Lady is a nice person.

                            But...

                            If a person is that incredulous about mathematics (with little apparent knowledge of the subject), it is not surprising that person is incredulous about age, history, and evolution (again with little apparent knowledge of the subjects).

                            "Incredible".

                            K54

                            P.S. This is no worse than I would be treated in a Fundy Christian church on "evilution", even though I'm not ignorant of their theology.

                            Comment


                            • Originally posted by 37818 View Post
                              well my first computer gave infinity as the answer.
                              [ATTACH=CONFIG]3783[/ATTACH]

                              And the default Android calculator also gives infinity as the answer for division by zero.
                              "Infinity" (sideways "8" - LOL) is not a number. How many times do you need to be told that? Aleph_null?

                              Your calculator simply reached the limit of its registers.

                              K54

                              Comment


                              • Originally posted by klaus54 View Post
                                That's your opinion. I'm sure Cat Lady is a nice person.

                                But...

                                If a person is that incredulous about mathematics (with little apparent knowledge of the subject), it is not surprising that person is incredulous about age, history, and evolution (again with little apparent knowledge of the subjects).

                                "Incredible".

                                K54

                                P.S. This is no worse than I would be treated in a Fundy Christian church on "evilution", even though I'm not ignorant of their theology.
                                There's nothing dumb about Teal, but there definitely is something dumb about this post of yours.

                                Stop turning this thread into a discussion about evolution.

                                Comment

                                Related Threads

                                Collapse

                                Topics Statistics Last Post
                                Started by Hypatia_Alexandria, 03-18-2024, 12:15 PM
                                48 responses
                                136 views
                                0 likes
                                Last Post Sparko
                                by Sparko
                                 
                                Started by Sparko, 03-07-2024, 08:52 AM
                                16 responses
                                74 views
                                0 likes
                                Last Post shunyadragon  
                                Started by rogue06, 02-28-2024, 11:06 AM
                                6 responses
                                48 views
                                0 likes
                                Last Post shunyadragon  
                                Working...
                                X