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::::I have already answered each of your questions earlier. The question about the ___location of irrational numbers written in the decimal positional system is impossible. The matrix contains an infinite number of infinite sequences of rational numbers. If you write down in a sequence of numbers, the numbers that arise step by step during the creation of a new number, which the diagonal method offers, then a sequence of rational numbers will be created, i.e. such a sequence as are in the matrix. You are asking about creating a list, I have previously indicated a link on how to write down the numbers from the matrix into a single list. You can also do this; A1 B1 A2 C1 B2 A3 D1 C2 B3 A4 E1 D2 ... However, if you learn how a matrix is built, and how a new number is created in the diagonal method, you will understand that this method is pointless, i.e. it will not create a new number that is not in the matrix. Now a question for you; 1. Can the diagonal method create an irrational number or an infinite sequence of rational numbers? 2. If the list does not contain all the numbers, will the diagonal method find a new number that is not on the list? I apologize if something was misunderstood, maybe it's because of Google Translate. [[User:Krzysztof1137|Krzysztof1137]] ([[User talk:Krzysztof1137|talk]]) 17:21, 21 April 2025 (UTC)
:::{{Re|Krzysztof1137}} ''"The matrix was created only to contradict the diagonal method."'' So it failed.<br>Apparently you confuse 'a possibility of expanding the decimal number infinitely' with 'having an infinite decimal number'. You certainly can find an arbitrarily long sequence of 3's after a decimal point in your table. But each such sequence is located in some specific row of the table and the number of the row determines how many threes there is in the sequence. You may have an infinite set of rows, but the ordinal number of each specific row is some natural number, which is certainly finite. As a result none of those sequences represents {{math|1/3}}. You definitely can find arbitrarily accurate aporoximations of one-third in your table, but not ''the'' {{math|1/3}} (let alone {{math|1/{{sqrt|3}}}}). --[[User:CiaPan|CiaPan]] ([[User talk:CiaPan|talk]]) 20:50, 21 April 2025 (UTC)
::::Now a question for you; 1. Can the diagonal method create an irrational number or an infinite sequence of rational numbers? 2. If the list does not contain all the numbers, will the diagonal method find a new number that is not on the list? [[User:Krzysztof1137|Krzysztof1137]] ([[User talk:Krzysztof1137|talk]]) 20:59, 21 April 2025 (UTC)
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