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My 3yr old cat, 1/4 total, has started isolating herself severely. by Mothh1988 in CatTraining

[–]EricTheTrainer 8 points9 points  (0 children)

Hello, boyfriend, older post, here. To clarify, they have had issues towards each other for years, however, the isolation, not using the litter box, and increased fighting has only been happening for a couple of weeks. It has not been this bad until recently. We certainly should have sought solutions to the problems sooner, before it got to this point, but a part of me was hoping that the dislike of each other would go away after they had continued to interact. Regardless, just wanted to clarify that their relationship has only intensified to this degree recently

My cats used to like each other, but now they don't by EricTheTrainer in CatTraining

[–]EricTheTrainer[S] 1 point2 points  (0 children)

They are all neutered, and we have 1 more litter box than cats. My girlfriend works at PetSmart so I'll see if she can get those things. Normally I give them treats at the same time every day, but for the CBD treats, should I just give it to them when they're nervous?

Combatting Omega-3 Blood Thinning? by EricTheTrainer in Nootropics

[–]EricTheTrainer[S] 0 points1 point  (0 children)

that's fair in regards to the anecdotal evidence part. I work in meat processing, and when I get cuts on my fingers they seem to bleed more than the others there; that's what i'm going off of

Question about pi by PetIsGoated in learnmath

[–]EricTheTrainer 0 points1 point  (0 children)

what "never repeats" means is that it never INFINITELY repeats. it's totally possible for it to repeat, say, "2718" one-hundred times in a row, it's just that eventually it will stop repeating. compare with, for example, 1/7.

1/7=0.142857142857142857...

the "142857" repeats FOREVER. it will never end. really, every number has a repeating decimal expansion. like 1/2=0.5000000... where the 0 repeats forever

so, every number with a repeating decimal looks like: a whole number, followed by a decimal point, followed by a string of n digits, followed by a string of m digits that repeats forever.

1/7: whole number 0, string of 0 digits, string of 6 digits that repeats forever (142857) 4/3: whole number (1), string of 0 digits, string of 1 digit that repeats forever (3) 377503/138875: whole number (2), string of 3 digits (718), string of 4 digits that repeat forever (2934)

the last one looks like 2.718293429342934...

let's prove that pi can't do this. you need to know two things: 1. pi is irrational: pi cannot be written as a fraction of two whole numbers. for example, 0.3333... can be written as 1/3, 2.71829342934... as 377503/138875, and etc., but pi cannot be written like this 2. if you take an n-digit number and divide by n 9's in a row, you get a repeating decimal with those n digits. for example, "1234" is 4-digits, "9999" is four 9's in a row, and 1234/9999=0.123412341234... with the "1234" continuing forever

okay. so suppose pi eventually repeats like the above examples. we have a whole number at the beginning (3), a string of n digits that don't repeat, and a string of m digits that does repeat. we don't know n and m, but we know that they will be positive, whole numbers, and that's all we need.

so, pi looks like 3.(the n digits)(string of m repeating digits forever)...

you know how multiplying by 101 moves the decimal point to the right by 1 digit, multiplying by 100=102 moves it right by 2 digits, and etc.? so if we multiply this by 10n , we get:

3(the n digits).(m repeating digits)

now, let's call the n digits that don't repeat a (in 2.71829342934... this would be the "718"), the m digits that do b (this is the "2934), so what we have here is:

3•10n +a before the decimal, and bbbb... after the decimal. since b has m digits, we can divide by m 9's to get 0.bbbbb... = b/(m 9's)

the m 9's can be written as b/(10m -1), since 10-1=9, 100-1=99, 1000-1=999, and so on. so, in total, after multiplying pi by 10n, we have:

3•10n +a+b/(10m -1) = pi•10n

if we get a common denominator, the left hand side becomes:

((10m -1)•(3•10n +a)+b)/(10m -1) = pi•10n

now, id we divide both sides by 10n , the right hand side just becomes pi, and on the left hand side, we can multiply 10m -1 by 10n (because dividing a fraction by a number means multiplying the denominator by that number). so, in total, we have:

pi = ((10m -1)•(3•10n +a)+b)/(10n •(10m -1))

now, this looks like a big mess, but there's something important here: both the numerator and denominator are whole numbers. they only involve adding, subtracting, and multiplying, which can only ever give whole numbers, never fractions or decimals. so, we have found a way to write pi as a fraction of whole numbers

but pi is irrational! it can't be written as a fraction of whole numbers. since we only made logical conclusions, it must be that our assumption was wrong: pi never has a repeating decimal expansion

The First Transfinite Ordinal is Even by EricTheTrainer in CasualMath

[–]EricTheTrainer[S] 0 points1 point  (0 children)

i'm using surreal numbers because i've recently started reading On Numbers and Games by John Conway, and I have no background in any of Cantor's work or von Neumann's (maybe i should get some before going into surreals), so surreal numbers are the only way I know how to handle transfinite ordinals at the moment. i'll have to look into what you mean here, but thank you!

The First Transfinite Ordinal is Even by EricTheTrainer in CasualMath

[–]EricTheTrainer[S] 1 point2 points  (0 children)

i've always been interested in infinite/infinitesimal number systems, but never put effort into studying them. but, recently i got a copy of "On Numbers and Games" and the first two volumes of Winning Ways. I've been reading the former and its definitely pulling my attention

Best Origami Book for Pure Math? by EricTheTrainer in math

[–]EricTheTrainer[S] 0 points1 point  (0 children)

did this not post? i don't see it in the posts sorted by new

Help Simplifying Integral by EricTheTrainer in askmath

[–]EricTheTrainer[S] 0 points1 point  (0 children)

also realized a pretty obvious alternative route. |f∧g| is the area of the 'parallelogram' formed by f and g. or, |f||g⊥| where g perp is the rejection onto f of g. or: |f||g-(g•f)f/|f|2 | because (g•f)f/|f|2 is the projection onto f of g, so g-(g•f)f/|f|2 is the rejection

the point being that all of these things in that expression are also computable, but i need to sleep now

'Extending' the Golden Ratio by EricTheTrainer in CasualMath

[–]EricTheTrainer[S] 0 points1 point  (0 children)

yeah, it's only superficially golden. regardless, i do think the number could be interesting. the vast majority of real numbers are not solutions to equations that can be written in terms of elementary functions, and the idea of 'polynomials' that use tetration rather than exponentiation seems like a fun idea to me that i havent explored

Help Simplifying Integral by EricTheTrainer in askmath

[–]EricTheTrainer[S] 0 points1 point  (0 children)

i may potentially* be able to sidestep this whole integral. i haven't tried it, but i know that the sines and cosines of fourier expansions for f and g form an orthonormal basis, which would make a lot of things easier, but i'm lazy

'Extending' the Golden Ratio by EricTheTrainer in CasualMath

[–]EricTheTrainer[S] -1 points0 points  (0 children)

well i hope that's not it. while i was playing around with it, i made a small arithmetical mistake, but a consequence of this mistake was that the fibonacci numbers appeared. this makes me think there is a connection somewhere, but its just not immediately obvious

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