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Directly proof $S$ is countable, where $S$ is set of function from $\{0, 1\}$ to $\mathbb{N}$
Suppose $S=\{f_1,f_2,f_3,f_4,f_5,........\}$ where $f_i$ is a function $f:\{0, 1\}\to\mathbb{N}.$ I have to prove $S$ is countable.Then need to prove direct one-to-one correspondence between $S$ and $\...
user976798
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Let set A is subset of set $\{{1,2,3,...,100}\}$ which has $55$ different elements.
Let set $A \subset\{{1,2,3,...,100}\}$ with $55$ distinct elements.
Prove that there exist two elements in $A$ which have a difference of 10.
I understand that the common thing is that we take more ...
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Natural Number Inductive Proof
Prove the following statement:
For every $\lambda$>1, there exists a number a��N and b∈[0,1) such that $\lambda$=a+b.
I first defined a = sup{n ∈ N | n ≤ x}, so m is the integer part of x or the ...
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