too lazy to find a header image

Is this true in arbitrary base?

I do not have any sources for that, so i cannot say… sorry!

it can’t be true in arbitrary base because positive integers always start with the same digit in binary, that digit being 1.

I think the original statement needs to be modified somehow to exclude n=0? like, as written I think it is false. anyway this sounds cool! I’m interested in what the proof is like.

I think the right generalization to arbitrary base is something like "if n > 0, then for any b > 2, 2^n, 3^n, ..., and (b-1)^n cannot all have the same leading digit." I'm not sure if this is true in the general case because I think the proof of the base 10 version uses something about 2^n * 5^n = 10^n to only have to worry about 3 being the leading digit (but not sure if that's the right approach I haven't actually worked it out yet)

wait, what? this statement doesn’t make sense for the base 3 case, where it would be saying 2^n cannot have the same leading digit as itself for all n > 0. you also have a counterexample very quickly in base 4, as 2^4 and 3^4 give you 100_4 and 1101_4, respectively.

it's only true in bases that aren't prime powers

There should be two of these. They're part of a magic trick where you split a 7 of diamonds into two 3½s

if anyone would be so kind as to scroll through this person's entire blog and count all the poll distributions

you have travelled too far back in time. please scroll back up to return the earth to its normal state

This reminds me of a joke I have with two of my cousins

this reminds me of two jokes i have with three of your cousins

This reminds me of the three jokes I have with four of our cousins

This reminds me of the joke i have with both of your moms

i wish i had that many oreos

I enjoy when video game mechanics fuck up in ways that provide insight into the particulars of their implementation. Like, my aerial controls just went screwy because somewhere below me there was a section of icy floor? Fascinating – let's see what other deranged implementation details I can puzzle out.

bugs are my favorite rule discovery puzzle game

i don’t need to say it

don’t say anything. just reblog this if you’re thinking of exactly that thing when you see this picture

If anyone wants to talk abstract algebra, hmu cause I love that shit and I REALLY want to talk about it more lol

which one? groups, rings, maybe even fields?

is there any subset of all undertale roleswap aus which form a permutation group?

depends on whether you count undertale itself as a roleswap au

In case you're not convinced enough that non-commutative algebra is super weird and fucked up: For a commutative monoid, being cancellative is sufficient to conclude that it is embeddable in a group. For a non-commutative monoid this is not the case!

fr? name an example

3.141592653589793238462643383279502884197169399375105820974944592307816406286208998628034825342117067982148086513282306647093844609550582231725359408128481117450284102701938521105559644622948954930381964428810975665933446128475648233786783165271201909145648566923460348610454326648213393607260249141273724587006606315588174881520920962829254091715364367892590360011330

omg i can't believe they're died.

quirky fourth wall breaking character but theyre just fucking. wrong about the medium theyre in. they keep making references to cinematic techniques and directorial styles and the other fourth wall breaking character is like "dumbass we're in a fucking comic book" and they are in a video game.

Well currently they’re in a tumblr post but I see your point

we're actually in a youtube video if this turns out to be funny enough

so obviously we need to make one version from each character's POV

i want to see a digital word game that lets you do this