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16h
accepted Is this basic fact about prime pairs obvious?
16h
comment Is this basic fact about prime pairs obvious?
@lulu please explain in an answer if you dare.
16h
comment Is this basic fact about prime pairs obvious?
Please turn your comments into answers if you think you have one.
16h
asked Is this basic fact about prime pairs obvious?
1d
accepted Elementary Twin Prime Attempt.
1d
revised Elementary Twin Prime Attempt.
deleted 50 characters in body
1d
revised Elementary Twin Prime Attempt.
added 132 characters in body
1d
revised Elementary Twin Prime Attempt.
added 413 characters in body
1d
comment Elementary Twin Prime Attempt.
Doesn't it though? By the pigeonhole principle. If there are an infinite number of pairs with difference less than $N$ then for some $X\lt N$ there must be an infinite number or else there is only a finite number of such pairs.
1d
revised Elementary Twin Prime Attempt.
deleted 1 character in body
1d
revised Elementary Twin Prime Attempt.
added 4 characters in body
1d
asked Elementary Twin Prime Attempt.
2d
accepted What phenomenon is this? $(2\Bbb{Z} + 1)\cup 3\Bbb{Z} = 2\Bbb{Z} \cup 3\Bbb{Z} + 3$
2d
comment What phenomenon is this? $(2\Bbb{Z} + 1)\cup 3\Bbb{Z} = 2\Bbb{Z} \cup 3\Bbb{Z} + 3$
How do you generalize this though and by that I mean apply to a wider range of sets?
2d
comment What phenomenon is this? $(2\Bbb{Z} + 1)\cup 3\Bbb{Z} = 2\Bbb{Z} \cup 3\Bbb{Z} + 3$
I mean by $A + x := A + \{x\} = \{ a + x: a \in A \}$.
2d
asked What phenomenon is this? $(2\Bbb{Z} + 1)\cup 3\Bbb{Z} = 2\Bbb{Z} \cup 3\Bbb{Z} + 3$
2d
accepted For two periodic sets $A,B$, $A \cup (B + \{x\}) = \{y\} + A \cup B$ for some $y \in \Bbb{N}$.
2d
comment For two periodic sets $A,B$, $A \cup (B + \{x\}) = \{y\} + A \cup B$ for some $y \in \Bbb{N}$.
Or under what conditions do you think it's true if ever?
2d
comment For two periodic sets $A,B$, $A \cup (B + \{x\}) = \{y\} + A \cup B$ for some $y \in \Bbb{N}$.
What if $x$ is constrained to be in $B$?
2d
asked For two periodic sets $A,B$, $A \cup (B + \{x\}) = \{y\} + A \cup B$ for some $y \in \Bbb{N}$.