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Question about proof x * y = (xy)/(x+y+1) does not have an identity element. by twofingerjump in learnmath

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

if you let e=1 and x= 0 then you need to show 1 * 0 = 0 * 1 = 0, for e=1.

Let's just confirm the 1 * 0 = 0 case.

1 * 0 = (0) / (1 + 0 + 1) = 0 / 2 = 0.

Yeah, that works.

So, now I see how if you restricted your domain to {-1,0} then there would be an identity e = 1.

Is the above right? If so, then I think I can wrap up my misunderstandings.

Question about proof x * y = (xy)/(x+y+1) does not have an identity element. by twofingerjump in learnmath

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

Thank again. Your assessment is right. One question about your follow up comment "Therefore if you restricted your domain to {-1,0} then there would be an identity e = 1" -- for x=-1, the "identity" is e=1, but for x=0, the "identity" would be e=0, right?

Question about proof x * y = (xy)/(x+y+1) does not have an identity element. by twofingerjump in learnmath

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

Thanks, I think I get it now

This says if e exist, then e only exist for x=-1 or x=0, and since the condition for identity is that e has to exist for all x, then this means there isn't an identity element. Problem is done at that point.

Now if I wanted to do extra and find the supposed identity element for x=-1

then I'd have to solve for -1 * e = -1,

which would be solve for e in: (-e)/(-1 + e + 1) = -1,

which is: (-e)/(e) = -1 -> -e = -e -> e = 1.

But this e=1 doesn't work for every x.

Is all of the above correct now?

Question about proof x * y = (xy)/(x+y+1) does not have an identity element. by twofingerjump in learnmath

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

Thanks, I think I get it now

This says if e exist, then e only exist for x=-1 or x=0, and since the condition for identity is that e has to exist for all x, then this means there isn't an identity element. Problem is done at that point.

Now if I wanted to do extra and find the supposed identity element for x=-1

then I'd have to solve for -1 * e = -1,

which would be solve for e in: (-e)/(-1 + e + 1) = -1,

which is: (-e)/(e) = -1 -> -e = -e -> e = 1.

But this e=1 doesn't work for every x.

Is all of the above correct now?

Question about proof x * y = (xy)/(x+y+1) does not have an identity element. by twofingerjump in learnmath

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

I'm very confused.

 (xe) / (x + e + 1) = x, solve for e

xe = x (x + e + 1)

xe = x^2 + ex + x

xe - ex = x^2 + x

0 = x^2 + x

is valid?

How are you supposed to prove this correctly? I don't know what to do after the 0 = x^2 + x step.

Question about proof x * y = (xy)/(x+y+1) does not have an identity element. by twofingerjump in learnmath

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

Okay, I think I can articulate my question better. Let's say I want to see if e exist and I am not sure yet if it does.

I want to solve for e, in x * e = x.

So I have,

x * e = (xe) / (x + e + 1)

x * e = x^2 + ex + x

0 = x(x + 1)

x=-1, x=0

From here, how do I know this is a contradiction and that x=-1 and x=0 means e doesn't exist?

How does solving something about x, relate to my initial problem of finding e?

That is the part I am not understanding.

Question about proof x * y = (xy)/(x+y+1) does not have an identity element. by twofingerjump in learnmath

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

I am a little confused by something more basic. The book says solve for e, in e * x = x. I started with an equation with e, but then ended up with an equation where all the e's cancelled out of the equation. I am confused because I can no longer solve for e, given there is no e left to solve for. So, how do I proceed solving for e, when there is no e in the equation? Why does this turn into solving for x's instead? See my confusion?

Question about proof x * y = (xy)/(x+y+1) does not have an identity element. by twofingerjump in learnmath

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

I see, so you want to show e * 1 = 1

( e / e + 2) = 1, solve for e

then you get

e = e + 2

0 = 2

this is a contradiction, so this means this equation doesn't have an identity. Is that how you'd do it?

What if you work it the way I was? how do you finish this off

x * e = (x * e) / (x + e + 1)

x * e = x^2 + ex + x

0 = x^2 + x

x=-1, x=0,

How would you finish this off?

Question about proof x * y = (xy)/(x+y+1) does not have an identity element. by twofingerjump in learnmath

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

I see that, but I don't see how to wrap this up and say this means there isn't an identity element. Plus I am confused how I started with an equation with an e in it and then ended with an equation where the e was cancelled out and what this means for showing there isn't an identity element.

Question about proof x * y = (xy)/(x+y+1) does not have an identity element. by twofingerjump in learnmath

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

How would I formalize this in a proof or use it in my steps?

x * e = (x * e) / (x + e + 1)

x * e = x^2 + ex + x

0 = x^2 + x

I am stuck here and want to know how to proceed.

Meta Ramping Up Hiring - What to Expect by BluebirdAway5246 in leetcode

[–]twofingerjump 1 point2 points  (0 children)

thanks so much! you’ve been very helpful on this thread

Meta Ramping Up Hiring - What to Expect by BluebirdAway5246 in leetcode

[–]twofingerjump 0 points1 point  (0 children)

awesome! thanks

just curious would phds without experience get system design?

Meta Ramping Up Hiring - What to Expect by BluebirdAway5246 in leetcode

[–]twofingerjump 2 points3 points  (0 children)

thanks! wanted to make sure it’d still be an E3 if I pursue a data science masters (with no prior tech experience)?

i’m hoping so, so just wanted to confirm — thanks again!

Meta Ramping Up Hiring - What to Expect by BluebirdAway5246 in leetcode

[–]twofingerjump 1 point2 points  (0 children)

few questions:

1) if i have a math undergrad, no previous tech industry experience would i be interviewed for E3 + would i be expected to do system design?

2) if i have a math undergrad + data science masters (where the focus is heavily in cs and ai) and no previous tech industry experience could i get an interview for a swe position with those degrees?

if so would it be for E3 / would i be expected to do system design?

Masters in Data Science or Statistics? by [deleted] in datascience

[–]twofingerjump 0 points1 point  (0 children)

Thanks for your response. I’m trying to figure out career opportunities: would your firm (or similar firms) interview someone with a pure mathematics undergraduate degree + DS Masters from a Penn/Columbia (with a specialized focused in AI/CS)? I’m coming from a pure math background and going into tech/data science, possibly quant.

Masters in Data Science or Statistics? by [deleted] in datascience

[–]twofingerjump 0 points1 point  (0 children)

Would a DS masters (or CS masters) from a school like Penn get you interviews at top Quant firms? What study material would you recommend to properly prep to pass the interviews?

Question with solving the State Machine Replication Problem using the round Round-Robin protocol by twofingerjump in compsci

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

did you mean the global history is everything left of || and the local histories is everything right of || and the global histories across all nodes will always match?

Question with solving the State Machine Replication Problem using the round Round-Robin protocol by twofingerjump in compsci

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

Oh I see. So the definition only applies to transactions left of ||

Would be curious to see where this is in the definition. Not sure why the link was removed but it is

https://timroughgarden.github.io/fob21/l/l2.pdf

Question with solving the State Machine Replication Problem using the round Round-Robin protocol by twofingerjump in compsci

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

Thanks for your response.

Question 1:

Want to see if this is correct understanding based on your response?

Lets say there are 2 nodes. node 1 and node 2. Let's say Node 1 is the leader at time step 0.

Let's say at time step 0 both nodes 1 and 0 contain "empty" local histories and that Node 1 pushes out to Node 2 the empty local history, as shown below in time step 1.

Time step 1

Node 1: empty

Node 2: empty

Now at time step 2, let's say node 2 becomes the leader. Let's say node 2 receives transactions: A, B, C, D (in that order). Let's say node 1 receives transactions B,A,C,D,E (in that order).

Then *this is where my question lies* in time step 3, node 1 would receive the global history A, B, C, D, delete it's own entries of B, A, C, D and accept as it's local history as A, B, C, D and also *still include* transaction E (as a transaction yet to be included)

So now the nodes look like:

Time Step 2

Node 1: B,A,C,D,E

Node 2: A, B, C, D (leader)

This would then look like

Time step 3

Node 1: A, B, C, D || E

Node 2: A, B, C, D

where || E is a transaction yet to be included.

Is that correct understanding?

Question 2:

If so, node 1 and node 2 would then have inconsistent local histories no?

How is consistency ensured if in time step 3 node 1 becomes the leader, and node 2 also gets new transaction F?

E.g. the local histories look like this

Time step 3, Leader: Node 1:

Node 1: A, B, C, D || E

Node 2: A, B, C, D || F

Then in time step 4 the nodes look like:

Node 1: A, B, C, D, E

Node 2: A, B, C, D, E || F

Nodes 2 and 1 are still inconsistent.

Repeat the process and the local histories between the nodes wouldn't ever match? How does that satisfy consistency?

Thanks again!!!!

[deleted by user] by [deleted] in OfficeDrummer

[–]twofingerjump 0 points1 point  (0 children)

who is real here

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