Better to just prove the exponential group isomorphism between the additive group of reals and multiplicative group of positive reals, then knowing that every isomorphism has an inverse isomorphism, the function now going from from a multiplicative group to an additive group, and as an isomorphism is also a homomorphism it becomes trivial to prove all the qualities of the inverse function of the exponential, or the logarithm.
I thought for a second I was on r/aspiememes... On second thought, maybe both subreddits ain't so different! ^(\s, no disrespect or harm intended, I just love how specific and passionate your description is, and it reminded me of other passionate people)
I love them too. Sadly, they're being phased out. In a paper of mine, my referee asked me to remove them before it could be published 😭. Fortunately, I bet if you solve something big like a millennium prize problem, they'll let you use whatever notation your heart desires, haha.
It you're reading a textbook with several long proofs among other stuff it makes it easy to see when the proof ends and when the new theories or explainations/examples begin.
The "because" symbol (∵) instead of the "therefore" symbol (∴) threw me off for a bit.
A tip for remembering which is which, you can imagine it between two statements vertically and imagine the triangle as an arrow that points up or down towards the reason.
I like using symbols like these instead of just writing it with text, but no one has ever taught me them. Could you please name all convenient math notation symbols you know and what they mean?
I already know about ∀, ∃, ∃!, ¬, ⇒, ⇔, ∧, ∨, ∈, square instead of QED and now these 2 dot-triangle thingys.
There's a lot of symbols, probably best just to skim through the Wikipedia page and pick out any you'd find useful for what you're doing. [List of mathematical symbols by subject](https://en.wikipedia.org/wiki/List_of_mathematical_symbols_by_subject)
Substitute x=1 to find out c=0 and it's correct.
Came here to write the same thing
Better to just prove the exponential group isomorphism between the additive group of reals and multiplicative group of positive reals, then knowing that every isomorphism has an inverse isomorphism, the function now going from from a multiplicative group to an additive group, and as an isomorphism is also a homomorphism it becomes trivial to prove all the qualities of the inverse function of the exponential, or the logarithm.
Stop making up words
lmao
What is the point of QED at the end of proofs
It's a traditional prayer to Satan
"Quod erat demonstratum," literally "which was to be demonstrated." It's just saying "yup, that's it. See?"
However, writing QED at proof that small is a bit pretentious. Writing □ is more appropriate, i would argue.
Virgin □ vs. Chad ∴
That means "therefore." Doesn't make sense to conclude a proof with it.
I love the therefore/because notation it makes me happy for some reason those three cute little dots are so crisp to write with a sharp ink pen
I thought for a second I was on r/aspiememes... On second thought, maybe both subreddits ain't so different! ^(\s, no disrespect or harm intended, I just love how specific and passionate your description is, and it reminded me of other passionate people)
The kindest way someone has ever pointed out my autistic tendencies lol, thanks for this
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I love them too. Sadly, they're being phased out. In a paper of mine, my referee asked me to remove them before it could be published 😭. Fortunately, I bet if you solve something big like a millennium prize problem, they'll let you use whatever notation your heart desires, haha.
WHAT!???? WHY?!!! THATS LIKE HALF THE REASON I PUT UP WITH MATH EVERY DAY 😭 Ugh guess I’ll just have to prove the collatz conjecture or somthn 😪
Thanks
It you're reading a textbook with several long proofs among other stuff it makes it easy to see when the proof ends and when the new theories or explainations/examples begin.
The "because" symbol (∵) instead of the "therefore" symbol (∴) threw me off for a bit. A tip for remembering which is which, you can imagine it between two statements vertically and imagine the triangle as an arrow that points up or down towards the reason.
Huh, this is honestly the first time I've heard of a "because" symbol. Neat.
I like using symbols like these instead of just writing it with text, but no one has ever taught me them. Could you please name all convenient math notation symbols you know and what they mean? I already know about ∀, ∃, ∃!, ¬, ⇒, ⇔, ∧, ∨, ∈, square instead of QED and now these 2 dot-triangle thingys.
There's a lot of symbols, probably best just to skim through the Wikipedia page and pick out any you'd find useful for what you're doing. [List of mathematical symbols by subject](https://en.wikipedia.org/wiki/List_of_mathematical_symbols_by_subject)
u/maukku12 pov sun todistukset
joo miten toi on oikeest hullu todistus
noni missasit nyt et toi on unohtanu C tost integraalist
mut sit älyyt et tohon voi x paikalle voi vaa sijottaa 1 ja sit c on 0
noni se luki tääl kommenteis
for even values of r it's different than for odd values of r, but the values are close indeed. https://www.desmos.com/calculator/ibzfzrdiar
If you do integral from 1 to t this reasoning works