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May
20
awarded  Scholar
May
20
comment Restricting a relation to an injective function
That's great, thanks! Since it's a graph theory problem it figures that it would be intactable without the big guns... :-(
May
20
accepted Restricting a relation to an injective function
May
18
revised Restricting a relation to an injective function
added 10 characters in body
May
18
revised Restricting a relation to an injective function
added 289 characters in body
May
18
comment Restricting a relation to an injective function
It can decide the existence question without constructing an injective function.
May
18
comment Restricting a relation to an injective function
Sounds prudent. But please add a comment to the effect that it's incorrect, so people won't have to read through the comments to figure it out.
May
18
comment Restricting a relation to an injective function
Equivalence is only true if $R$ is already a function.
May
18
comment Restricting a relation to an injective function
Let $A = \{a, b, c\}$, $R = \{ (a, 1), (a, 2), (a, 3), (b, 3), (c, 3) \}$.
May
18
revised Restricting a relation to an injective function
added 4 characters in body
May
18
comment Restricting a relation to an injective function
Nice try, but it just says that the domain and image of R must be of equal size. This is a necessary condition for a relation on finite sets, but not a sufficient one.
May
18
comment Does every uncountable subset of $\mathbb{R}$ have an uncountable closed subset?
@Jared, there are a couple of things wrong with your comment. You are right to infer that an uncountable subset of $\mathbb R$ must contain some irrational numbers, but that's not enough to answer the question in the negative. A set of exactly two irrational numbers is closed, for example, so your comment does not amount to a counterexample. Your second comment has more serious problems. No, that's not at all what "uncountable" means-- look it up. And the countability of the rationals in an interval is not, by any means, a consequence of non-continuity.
May
18
asked Restricting a relation to an injective function
May
11
revised Is there any way to define arithmetical multiplication as other thing than repeated addition?
corrected typo in the formula
May
11
suggested approved edit on Is there any way to define arithmetical multiplication as other thing than repeated addition?
May
11
comment Is there any way to define arithmetical multiplication as other thing than repeated addition?
Indeed: handling the carry requires addition. I'd have preferred to write "a definition that makes no reference to addition", but that's not the case. But the repeated-addition aspect is well and truly gone.
May
10
revised Is there any way to define arithmetical multiplication as other thing than repeated addition?
added 86 characters in body
May
9
answered Is there any way to define arithmetical multiplication as other thing than repeated addition?
May
9
answered How many binary strings of length 2n + 1 have more 1's than 0's? Use bijection to prove.
May
8
comment Finding an circle inside distribution of elemets
Actually there's an even easier way to find the (approximate) center: Average the x coordinate of all points to get the center's x coordinate, and similarly for y.