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==Re: Determinant 1==
Sorry about revising the revision on the Modular Group page; i hit submit without adding a comment; the reason unit determinant differs from determinant 1 is that in a ring (such as the ring of all 2x2 matrices, or in this case Z), a unit is anything invertible. In particular, the original reading could lead to an interpretation that the determinant was 1 or -1, which if you remove the identification criterion, reads as a quotient of GL2Z rather than SL2Z. The example I gave had determinant 1, but I meant it to have determinant -1, whoops!

Sorry if this isn't the place to chat with a user, I'm not super well-versed with this :)


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https://en.wikipedia.org/wiki/Kepler's_laws_of_planetary_motion
https://en.wikipedia.org/wiki/Kepler's_laws_of_planetary_motion


== Happy First Edit Day! ==
== You reverted the changed I made on the page about the geometric series ==

The geometric series section on repeating decimals was incorrect, even listing the formula incorrectly as (a/1-r) equaling the sum of r^n with respect to n, when it already acknowledged that the series is instead equal to a-r^n/1-r. You must include the infinitesimal difference in expressions of infinitesimals.

: There is no number "n" in 0.7777..., which is an infinite sum equal to (not approximately equal to, or essentially equal to) 7/9. Per [[WP:BRD]], do not restore your edit without consensus; but there will not be consensus for introducing a [[WP:FRINGE|fringe]] view about the meaning of decimal notation to the article. --[[User:JayBeeEll|JBL]] ([[User_talk:JayBeeEll|talk]]) 17:38, 13 September 2020 (UTC)

::Thanks {{u|JayBeeEll|JBL}} I couldn't have said it better myself.--[[User:Wcherowi|Bill Cherowitzo ]] ([[User talk:Wcherowi#top|talk]]) 21:30, 13 September 2020 (UTC)

:::To say .7 repeating equates to 7/9 is foolish. The fact that it goes to the bounds of infinity with 7*10^-n as n approaches infinity accounts for infinitesimals, and yet you say infinitesimals are equal to 0. What's the limit of .9 repeating ^10^n as n approaches infinity? 1/e. What's the limit of 1^10^n as n approaches infinity? 1. You acknowledge infinitesimals in your infinite summation, and then say they don't exist. Which is it? Do you do the same with complex numbers? Do you say 1+i is exactly equal to 1? Approaching does not mean equal.

::::Infinitesimals do not exist in the field of real numbers as they do not satisfy the [[Archimedean property]]. If you want to include them, then you are not talking about real numbers and are indulging in non-standard analysis. This is all well and good, but please learn the subject before subjecting me to more of your prattle.--[[User:Wcherowi|Bill Cherowitzo ]] ([[User talk:Wcherowi#top|talk]]) 19:57, 15 September 2020 (UTC)

:::::You are correct in that they do not exist in the field of real numbers, but neither does .9 repeating. One can't just express a number with an infinitesimal difference and then say that, since infinitesimals don't exist in real numbers, that it's equal to the original number, with no difference. The geometric series here HAS an infinitesimal if you create in infinite sum. Not only is one subtracted, there are also infinitely many added to make the repeating number. Here's an analogy. e^ix = cosx + isinx. You are essentially saying e^ix = cosx because i isn't real. You include nonstandard analysis by creating a repeating number and using the geometric series to an infinite value, and then ignore a part of nonstandard analysis by saying it's not real. Call it whatever you want, you still included infinitesimals, and then ignored others. [[User:Bigparsely|Bigparsely]] ([[User talk:Bigparsely|talk]]) 20:22, 16 September 2020 (UTC)

== Edit integration by substitution ==

You reverted two edits I made on the article on Integration by substitution. I believe the edits were correct and would like to see if we can agree.

In the statement of a theorem concerning subsitution in definite integrals and its proof, the formulation "if {{math|''u'' {{=}} ''φ''(''x'')}}" occurred. I submit that even if we may say something like that when explaining to beginner students, it actually makes no sense. The integral <math display="inline">\int_a^b f(\varphi(x))\varphi'(x)\, dx </math> is some number by the definition of the Riemann integral, and equally <math display="inline">\int_{\varphi(a)}^{\varphi(b)} f(u)\,du</math>, being the integral over the function ''f'' on the interval <math display="inline">[\varphi(a),\varphi(b)]</math>, is some number. The content of the theorem is then that these numbers happen to be equal. Note that we could equally well state
:<math>
\int_a^b f(\varphi(x))\varphi'(x)\, dx = \int_{\varphi(a)}^{\varphi(b)} f(x)\,dx.
</math>


Would you explain that by saying <math display="inline"> \varphi(x)= x </math>?

[[User:MathHisSci|MathHisSci]] ([[User talk:MathHisSci|talk]]) 20:45, 27 October 2020 (UTC)
==[[Permutations#Permutations_with_repetition|Permutations with repetition]]==
It is a very tortured way and also it is stated when it is said there "in general they are not permutations" Check the formula k^n as is all the possible tuples made with the elements of a second set. The decimal numeric system is an example: you have a set of 10 symbols 0..9 so all the possible 3-tuples from the set 0,1,2,...,9 are 000,001,002,003,010,011,012,...,999 so 10^3 tuples is only the plural of [[tuple]]: ordered list. The least to do to clarify is change '''tuples''' to '''tuples of set S''' [[User:Orendona|Orendona]] ([[User talk:Orendona|talk]]) 22:26, 1 November 2020 (UTC)
==[[Permutations#Permutations_with_repetition|Permutations with repetition]]==
The problem is that Permutations with repetition are not permutations. That also is stated in the article, It is a probability scalar number as it is used [[User:Orendona|Orendona]] ([[User talk:Orendona|talk]]) 11:23, 4 November 2020 (UTC)

https://www.ck12.org/probability/permutations-with-repetition/lesson/Permutations-with-Repetition-BSC-PST/#:~:text=There%20is%20a%20subset%20of,of%20objects%20that%20are%20identical.
https://brilliant.org/wiki/permutations-with-repetition/
https://www.mathsisfun.com/combinatorics/combinations-permutations.html
https://www.google.com/search?q=Permutations+with+repetition&oq=Permutations+with+repetition&aqs=chrome..69i57j0l4j69i60l3.9800j0j1&sourceid=chrome&ie=UTF-8




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Latest revision as of 19:35, 10 August 2024

Re: Determinant 1

[edit]

Sorry about revising the revision on the Modular Group page; i hit submit without adding a comment; the reason unit determinant differs from determinant 1 is that in a ring (such as the ring of all 2x2 matrices, or in this case Z), a unit is anything invertible. In particular, the original reading could lead to an interpretation that the determinant was 1 or -1, which if you remove the identification criterion, reads as a quotient of GL2Z rather than SL2Z. The example I gave had determinant 1, but I meant it to have determinant -1, whoops!

Sorry if this isn't the place to chat with a user, I'm not super well-versed with this :)

Warning Templates

[edit]

Information icon Hello. Regarding the recent revert you made to Fibonacci number: you may already know about them, but you might find Wikipedia:Template messages/User talk namespace useful. After a revert, these can be placed on the user's talk page to let them know you considered their edit inappropriate, and also direct new users towards the sandbox. They can also be used to give a stern warning to a vandal when they've been previously warned. Thank you.

Re: Kepler Fraud

[edit]

Thanks for revising my edit instead of deleting it. :) https://en.wikipedia.org/wiki/Kepler's_laws_of_planetary_motion

Happy First Edit Day!

[edit]
Hey, Wcherowi. I'd like to wish you a wonderful First Edit Day on behalf of the Wikipedia Birthday Committee!Have a great day!

Brachy08 (Talk) 09:59, 10 August 2023 (UTC)[reply]

Happy First Edit Day!

[edit]
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