User talk:DoronSahdmi: Difference between revisions
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According to the Axiomatic Set theory, a non-empty Set is a collection of objects, where each object is clearly distinguish from the rest of the objects. |
According to the Axiomatic Set theory, a non-empty Set is a collection of objects, where each object is clearly distinguish from the rest of the objects. |
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The |
The property of being clearly distinguished exists in the foundations of the axioms that define any member on the real-line, no matter if it is a Natural, a Rational or an Irrational number. |
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In other words, there is an unbreakable connection between being clearly distinguished and the ability to define the quantity and location (order) that each member has along the real-line, no matter what representation method is used. |
In other words, there is an unbreakable connection between being clearly distinguished and the ability to define the quantity and location (order) that each member has along the real-line, no matter what representation method is used. |
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In that case (when using only the minimal condition as mentioned above) Cantor's second diagonal argument does not hold. |
In that case (when using only the minimal condition as mentioned above) Cantor's second diagonal argument does not hold. |
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Furthermore, the necessity to use infinitely many symbols in order to represent a member like PI, actually tells us that we use an inaccurate representation method for some irrational number (the reason is very simple, because each base value in the place value method is a natural number > 1, and no irrational number can be represented by a finite string that is the result of a ratio |
Furthermore, the necessity to use infinitely many symbols in order to represent a member like PI, actually tells us that we use an inaccurate representation method for some irrational number (the reason is very simple, because each base value in the place value method is a natural number > 1, and no irrational number can be represented by a finite string that is the result of a ratio between natural numbers). |
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Cantor ignored these simple facts, and as a result its argument is based on a representation method and not on the mathematical objects themselves, in this case. |
Cantor ignored these simple facts, and as a result its argument is based on a representation method and not on the mathematical objects themselves, in this case. |
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Furthermore, since any number is not less then a quantity and an order along the real-line, we have no choice but to write down in the side that represents the set's members, every set's member, which is less or equal to the number that was written in the proper sub-set column. For example let us re-examine the mapping that exists between the set of Natural numbers and its proper subset of even numbers. |
Furthermore, since any number is not less then a quantity and an order along the real-line, we have no choice but to write down in the side that represents the set's members, every set's member, which is less or equal to the number that was written in the proper sub-set column. For example let us re-examine the mapping that exists between the set of Natural numbers and its proper subset of even numbers. |
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If the set of even numbers is a proper |
If the set of even numbers is a proper sub-set of the set of Natural numbers, then each even number is also a member of the set of Natural numbers. |
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In that case, if some even number is in the proper sub-set of the even numbers, it is also in the set of the Natural numbers, and we have no choice but to write down in the column that represents the Natural numbers, any single Natural number that is less or equal to the even number that was written in the side that represents the even numbers: |
In that case, if some even number is in the proper sub-set of the even numbers, it is also in the set of the Natural numbers, and we have no choice but to write down in the column that represents the Natural numbers, any single Natural number that is less or equal to the even number that was written in the side that represents the even numbers: |
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1 <--> 2 |
1 <--> '''2''' |
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5 <--> 10 |
5 <--> 10 |
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6 <--> 12 |
6 <--> '''12''' |
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... |
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Since each Natural number is not less than a cardinal and an ordinal that is clearly distinguished from the rest of the Natural numbers, and since each member of a proper |
Since each Natural number is not less than a cardinal and an ordinal that is clearly distinguished from the rest of the Natural numbers, and since each member of a proper sub-set is also a member of the set, there cannot be a bijection between a set and its proper sub-set (as shown above). |
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In the case of the proper sub-set of even numbers and the set of Natural numbers, there exists a permanent ratio of 1 to 2 that prevents the bijection. |
In the case of the proper sub-set of even numbers and the set of Natural numbers, there exists a permanent ratio of 1 to 2 that prevents the bijection. |
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There can be a bijection between two non-finite sets only if they are disjoined in any recursion level. |
There can be a bijection between two non-finite sets only if they are disjoined in any recursion level. |
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Some claims that the property of a set is the result of the membership between members, so a set's property defined by its membership. But as I showed, there is a property which is not the result of the membership but it is actually its reason, and this reason is based on the A prioristic uniqueness of each set's member, which defines A priori the property of any non-empty set. |
Some claims that the property of a set is the result of the membership between members, so a set's property defined by its membership. But as I showed, there is a property which is not the result of the membership but it is actually its reason, and this reason is based on the A prioristic uniqueness of each set's member, which defines A priori the property of any non-empty set. [[User:DoronSahdmi|DoronSahdmi]] 17:26, 4 November 2006 (UTC) |
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==File source problem with File:No 1.jpg== |
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[[File:Copyright-problem.svg|64px|left]] |
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Thank you for uploading '''[[:File:No 1.jpg]]'''. I noticed that the file's description page currently doesn't specify who created the content, so the [[copyright]] status is unclear. If you did not create this file yourself, you will need to specify the owner of the copyright. If you obtained it from a website, please add a link to the website from which it was taken, together with a brief restatement of that website's terms of use of its content. However, if the copyright holder is a party unaffiliated from the website's publisher, that copyright should also be acknowledged. |
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== [[:File:Base23.jpg]] missing description details == |
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<div style="padding:5px; background-color:#E1F1DE;">'''Dear uploader:''' The media file you uploaded as: |
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*[[:File:Base23.jpg]] |
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is missing a description and/or other details on its image description page. If possible, please add this information. This will help other editors make better use of the image, and it will be more informative to readers. |
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Latest revision as of 04:41, 22 January 2014
Image tagging for Image:No 1.jpg
[edit]Thanks for uploading Image:No 1.jpg. The image has been identified as not specifying the source and creator of the image, which is required by Wikipedia's policy on images. If you don't indicate the source and creator of the image on the image's description page, it may be deleted some time in the next seven days. If you have uploaded other images, please verify that you have provided source information for them as well.
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This is an automated notice by OrphanBot. For assistance on the image use policy, see Wikipedia:Media copyright questions. 21:09, 11 September 2006 (UTC)
Hello Moderator,
My name is Doron Shadmi and I am the source and creator of this image.
Thank you.
New mathematical framework
[edit]If you really want to discuss your "new framework" and its impact on 0.9999...=1, feel free to do so on my talk page. I would appreciate an explanation of some of your definitions, actually starting with definition 1:
"Definitinon 1: A is a common property of x xor y."
What is defined here? A? Being a common property of x xor y? What is "common property of x xor y" supposed to mean? I would believe "x xor y" to be a statement which is either true or false, but then what's a common property of a statement? On an even more basic level, what are x and y (and A, if that's not what is being defined)?
But I do believe that right now, your new framework is not yet ready for either publication in a journal or Wikipedia; thus, if I may offer a piece of advice, I wouldn't bother the experts at the arguments page. Yours, Huon 20:24, 14 September 2006 (UTC)
Hi Huon,
Please look again at definition 1 DoronSahdmi 16:58, 4 November 2006 (UTC)
Some notions
[edit]A person cannot be considered as a professional mathematician if he cannot distinguish between a mathematical object and its representation.
According to the Axiomatic Set theory, a non-empty Set is a collection of objects, where each object is clearly distinguish from the rest of the objects.
The property of being clearly distinguished exists in the foundations of the axioms that define any member on the real-line, no matter if it is a Natural, a Rational or an Irrational number.
In other words, there is an unbreakable connection between being clearly distinguished and the ability to define the quantity and location (order) that each member has along the real-line, no matter what representation method is used.
For example, by using the place value representation method we can represent the real-line's member PI in infinitely many ways that are different from each other by the their base value. No one of these representations is the mathematical object PI.
If we wish to prove something about the mathematical objects, we have to use an extra care not to mix up between them and any possible representation of them.
By using this insight, let us re-examine the famous Cantor's second diagonal argument.
As a fundamental approach, we have to use the minimal condition that exists in some collection of mathematical objects that is considered as a non-empty set. This minimal condition is exactly the property of each mathematical object, which enables to find its exact quantity and location (order) along the real-line.
In that case we actually can represent each real-line's member by a finite and unique string of symbols (as we did in the case of PI).
In that case (when using only the minimal condition as mentioned above) Cantor's second diagonal argument does not hold.
Furthermore, the necessity to use infinitely many symbols in order to represent a member like PI, actually tells us that we use an inaccurate representation method for some irrational number (the reason is very simple, because each base value in the place value method is a natural number > 1, and no irrational number can be represented by a finite string that is the result of a ratio between natural numbers).
Cantor ignored these simple facts, and as a result its argument is based on a representation method and not on the mathematical objects themselves, in this case.
Some claims that the non-repeated pattern of infinitely-many symbols is an inherent property of any irrational number. In that case the exact value of an irrational number cannot be satisfied, which contradicts the basic notion of the Set concept (every set's member is A priori clearly distinguished from the rest of the members).
When defining the membership relations between non-empty sets, we have to understand each definition that is used in some argument, before we use it.
For example, if a proper sub-set is any non-empty set that fully included in some set, than each member of the sub-set is a member of the set.
If we examine the mapping between a set and its proper sub-set, then if some member is written in the column that represents the proper sub-set's members, it must be written also in the column that represents the set's members.
Furthermore, since any number is not less then a quantity and an order along the real-line, we have no choice but to write down in the side that represents the set's members, every set's member, which is less or equal to the number that was written in the proper sub-set column. For example let us re-examine the mapping that exists between the set of Natural numbers and its proper subset of even numbers.
If the set of even numbers is a proper sub-set of the set of Natural numbers, then each even number is also a member of the set of Natural numbers.
In that case, if some even number is in the proper sub-set of the even numbers, it is also in the set of the Natural numbers, and we have no choice but to write down in the column that represents the Natural numbers, any single Natural number that is less or equal to the even number that was written in the side that represents the even numbers:
1 <--> 2
2 <-->
…
1 <--> 2
2 <--> 4
3 <-->
4 <-->
…
1 <--> 2
2 <--> 4
3 <--> 6
4 <-->
5 <-->
6 <-->
…
1 <--> 2
2 <--> 4
3 <--> 6
4 <--> 8
5 <--> 10
6 <--> 12
7 <-->
8 <-->
9 <-->
10 <-->
11 <-->
12 <-->
...
Since each Natural number is not less than a cardinal and an ordinal that is clearly distinguished from the rest of the Natural numbers, and since each member of a proper sub-set is also a member of the set, there cannot be a bijection between a set and its proper sub-set (as shown above).
In the case of the proper sub-set of even numbers and the set of Natural numbers, there exists a permanent ratio of 1 to 2 that prevents the bijection.
There can be a bijection between two non-finite sets only if they are disjoined in any recursion level.
Some claims that the property of a set is the result of the membership between members, so a set's property defined by its membership. But as I showed, there is a property which is not the result of the membership but it is actually its reason, and this reason is based on the A prioristic uniqueness of each set's member, which defines A priori the property of any non-empty set. DoronSahdmi 17:26, 4 November 2006 (UTC)
File source problem with File:No 1.jpg
[edit]
Thank you for uploading File:No 1.jpg. I noticed that the file's description page currently doesn't specify who created the content, so the copyright status is unclear. If you did not create this file yourself, you will need to specify the owner of the copyright. If you obtained it from a website, please add a link to the website from which it was taken, together with a brief restatement of that website's terms of use of its content. However, if the copyright holder is a party unaffiliated from the website's publisher, that copyright should also be acknowledged.
If you have uploaded other files, consider verifying that you have specified sources for those files as well. You can find a list of files you have created in your upload log. Unsourced and untagged images may be deleted one week after they have been tagged per Wikipedia's criteria for speedy deletion, F4. If the image is copyrighted and non-free, the image will be deleted 48 hours after 10:23, 4 May 2010 (UTC) per speedy deletion criterion F7. If you have any questions or are in need of assistance please ask them at the Media copyright questions page. Thank you. Sfan00 IMG (talk) 10:23, 4 May 2010 (UTC)
Notification of automated file description generation
[edit]Your upload of File:Base23.jpg or contribution to its description is noted, and thanks (even if belatedly) for your contribution. In order to help make better use of the media, an attempt has been made by an automated process to identify and add certain information to the media's description page.
This notification is placed on your talk page because a bot has identified you either as the uploader of the file, or as a contributor to its metadata. It would be appreciated if you could carefully review the information the bot added. To opt out of these notifications, please follow the instructions here. Thanks! Message delivered by Theo's Little Bot (opt-out) 12:53, 21 January 2014 (UTC)
File:Base23.jpg missing description details
[edit]is missing a description and/or other details on its image description page. If possible, please add this information. This will help other editors make better use of the image, and it will be more informative to readers.
If you have any questions, please see Help:Image page. Thank you. Message delivered by Theo's Little Bot (opt-out) 04:41, 22 January 2014 (UTC)