Basic Math

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7 hours ago, Jamie123 said:

The only solution I can think of is that "equality" in the statement x=i^i does not identify an equivalency, but a kind of "predicate" which applies not only to x but to other numbers as well.

I agree. In mathematics, "equality" generally means "identity", as you note. But when we say i^i={some value}, we are saying that it includes that value, not that it is identical to that value. We can still use the idea of identity when, for example, using a specific solution as the value in another expression, but we have to understand that the meaning of "=" is not the same as in 4+3=7. I'm sure someone has formalized this somewhere, but I've never really seen this topic addressed.

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9 hours ago, zil2 said:
On 1/20/2024 at 5:25 AM, Carborendum said:

But the truth of the matter is that, believe it or not, the answer really is 5!.

There, fixed that for you.

The editorial instinct is strong with this one.

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On 1/21/2024 at 12:31 AM, mikbone said:


I finally watched the end of this. It's interesting that Euler made exactly the same "mistake" Mr. Mind Your Decisions objected to, but got away with it because it would be "shattering the foundations of analysis" to think otherwise. It sounds very much like an argument by appeal to consequences. Sorry to keep going back to the UK Post Office shenanigans, but I think a lot of the arguments there were won that way: "Mrs. Goggins the postmistress is a woman of impeccable honesty and integrity, but the Post Office computer says she was stealing money. If we can't trust the Post Office, who can we trust? No one, that's who, and how terrible would that be? Therefore we must find Mrs. Goggins guilty of theft and send her to prison, and confiscate her house and all her savings to repay the shortfall by a 'proceeds of crime' order."

BTW I always refer to postmistresses as "Mrs. Goggins", because she was the postmistress in the popular kids' TV show Postman Pat. I have no idea whether real postmistresses find this offensive, but they shouldn't. Mrs. Goggins was a nice person, whom no one should object to being compared with.

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Mrs. Goggins

P.S. I've just noticed the the first time...ever...that Mrs. Goggins' glasses are a different distance apart than her eyes. So how does she look through them without making herself reverse cross-eyed?

Cross Eyed Illusion | Tutorial here:… | Flickr

Edited by Jamie123
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36 minutes ago, The Folk Prophet said:

My quibble isn't punctuation so much as... in what world is a factorial considered "Basic Math"?

Maybe he meant BASIC Math, and your quibble should be capitalization (or possibly the forum software converting everything to initial caps and the rest lower case). ;) :P

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Story time.

When I was in high school, Algebra I, Algebra II, and Geometry were required courses. Everyone had to take them.

I did quite well in Geometry, but had middling grades in Algebra I and actually came close to failing Algebra II. It should have been clear that despite my "gifted" label math was not my forte and I should not seriously consider any math classes going forward unless they were specific courses like the "Math and Money" course the high school was offering. 

One of my brothers, who was in graduate school, convinced my mom to sign me up for Pre-Calculus. 

The Pre-Calculus teacher would take 30 minutes of each 90 minute class to go desk by desk and grade our papers right then and there so that she didn't have to do any grading at home. As a result, we almost never got through the day's material and she could never understand how that kept happening. Instead, we were just supposed to attend before-school and after-school tutoring, which was almost always packed with students who needed the help and so it was rare to get any one-on-one assistance. 

My parents initially just blamed me for not keeping up, but fortunately in my depression I'd saved a copy of a paper where she wrote a message inviting me to leave the class. This was enough to trigger a parent-teacher conference with myself, my dad, the teacher, and the assistant principal. 

Suffice to say that the assistant principal was mortified by what he found out during that conference. 

I was switched to a different class entirely (a single-semester introduction to psychology course) for the spring semester, but the Pre-Calculus class damaged my GPA so much that I missed the top 10% by six slots... and with it the tens of thousands of dollars in state-level financial assistance I would have gotten because the state of Texas pays full tuition for all graduates of public in-state high schools who attend public in-state colleges. 

So yeah, because my parents listened to my brother instead of me, and because the teacher was too lazy to do anything at home, my life was altered for the worst. 

I think everyone here can understand why I do not like math despite being a business major, and instead chose to focus on marketing. 

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Yeah, math and I have a love-hate relationship too.  I'm a finance major, but that means my entire math brain is kept in spreadsheets, where all the work happens.

Homeschooling rocked, because I was blessed to be there and witness the exact moment my daughter surpassed her old man in math.  She was like 6 or 7.  I was introducing her to 3rd grade addition problems.  Adding lots of numbers together all at once.


I was going row by row, showing her how the stuff she already knew could be used.   You already know 4+3, it's what?  Seven.  Yep, so just add 2 to 7, and write it at the bottom of the first column.   

I asked her a question about the 2nd column, and she thought for a minute and said "It's 1399!"  I asked her what she meant, and she said it was the answer to the whole problem.  I quickly did the rest of the math to discover she was correct, and asked her how she did it so fast.  She said it just worked that way in her head. 

That's when we moved to the "here's the assignment, ask me or mom if you need help" phase of math for her.   She basically got herself through algebra with occasional help from Mom.   To this day, I still count by internally singing those school house rocks videos in my head.  Dang smart kid. 

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8 hours ago, The Folk Prophet said:

My quibble isn't punctuation so much as... in what world is a factorial considered "Basic Math"?

Isn't it? 

I learned it in the same class as the order of operations.

Edited by Carborendum
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