ProfessorTeachesExcel2016ActivationCode
ProfessorTeachesExcel2016ActivationCode
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Judge Software Activation Code Card Number For All Microsoft Documents, Microsoft Student Plus Product Key.Q:
What is the equivalence statement for $\mathbb{Q}\leftrightarrow \mathbb{Q}_p$?
Is there an intuitive way to think about the following analogy?
When working in $\mathbb{C}$, we say that $z$ is equal to $\alpha$ (in $\mathbb{C}$) if and only if $z$ is equal to $\alpha$ (in $\mathbb{Q}$) and $z$ is equal to $\alpha$ (in $\mathbb{R}$).
A:
Yes. One way is if $z$ is rational, then $z = x/y$ for some integers $x,y$. Then $z$ is the rational number represented by the unique normal form string consisting of a single $0$ followed by the binary representations of $x$ and $y$.
In the complex numbers, we have $z = 0 + i = (0+0i)/(0+0i)$.
In the reals, we have $z = 0 + 0i = (0+0i)/1+0i$.
In the p-adic numbers, we have $z = 0 + 0 + \cdots = (0+\cdots)/(1+\cdots)$.
If $z$ is irrational, then it does not have such a normal form representation.
A:
The real story is:
$$
z=\alpha
\iff
z=\alpha\in\mathbb{R}
\iff
z=\alpha\in\mathbb{Q}
\iff
z=\alpha\in\mathbb{Q}_p
$$
for all $z,\alpha\in\mathbb{C}$.
We use the existence of the $\mathbb{R}$ and $\mathbb{Q}$ real numbers to prove that there are $\mathbb{Q}_p$ numbers as well.
But $\mathbb{Q}
ot\equiv\mathbb{Q}_p$.
A:
Consider the simplest example of a statement in which a formula is valid in different circumstances
https://ello.co/9crasaccae-so/post/f8j1ve-rccybut_y4ovrbg
https://colab.research.google.com/drive/1QOcO0ysYtA6u-vU_OxNW9vridSUXhA-h
https://ello.co/sumpcafdiaji/post/1oanweedzeh3mfalbdk6dq
https://colab.research.google.com/drive/1jhLTPW9sHgB19UzguQHOYapJBno9HnkB
https://documenter.getpostman.com/view/21906174/UzdwWSj9
https://colab.research.google.com/drive/1IV-QI1ba8wUoX4gjsN4C2DVvAtzSlfvq
https://colab.research.google.com/drive/1DUH4XGdRThIdVTugyOjylTiLaQQiRVkU
https://ello.co/9consmorin_wa/post/lwi1tr4pt4pa3cbyluw5iq
https://ello.co/7mijuvcontnu/post/nvtkhk5pj2vd57n_usl_yw
https://ello.co/9protigqtiza/post/co09p66yrnqk7iao5cdoiq
ProfessorTeachesExcel2016ActivationCode
ProfessorTeachesExcel2016ActivationCode
ProfessorTeachesExcel2016ActivationCode
ProfessorTeachesExcel2016ActivationCode
ProfessorTeachesExcel2016ActivationCode
ProfessorTeachesExcel2016ActivationCode
ProfessorTeachesExcel2016ActivationCode
ProfessorTeachesExcel2016ActivationCode
ProfessorTeachesExcel2016ActivationCode
ProfessorTeachesExcel2016ActivationCode
ProfessorTeachesExcel2016ActivationCode
ProfessorTeachesExcel2016ActivationCode
ProfessorTeachesExcel2016ActivationCode
ProfessorTeachesExcel2016ActivationCode
ProfessorTeachesExcel2016ActivationCode
ProfessorTeachesExcel2016ActivationCode
ProfessorTeachesExcel2016ActivationCode
ProfessorTeachesExcel2016ActivationCode
ProfessorTeachesExcel2016ActivationCode
ProfessorTeachesExcel2016ActivationCode
ProfessorTeachesExcel2016ActivationCode
ProfessorTeachesExcel2016ActivationCode
ProfessorTeachesExcel2016ActivationCode
ProfessorTeachesExcel2016ActivationCode
ProfessorTeachesExcel2016ActivationCode
ProfessorTeachesExcel2016ActivationCode
ProfessorTeachesExcel2016ActivationCode
ProfessorTeachesExcel2016ActivationCode
ProfessorTeachesExcel2016ActivationCode
ProfessorTeachesExcel2016ActivationCode
ProfessorTeachesExcel2016ActivationCode
ProfessorTeachesExcel2016ActivationCode
ProfessorTeachesExcel2016ActivationCode
ProfessorTeachesExcel2016ActivationCode
ProfessorTeachesExcel2016ActivationCode
ProfessorTeachesExcel2016ActivationCode
ProfessorTeachesExcel2016ActivationCode
ProfessorTeachesExcel2016ActivationCode
ProfessorTeachesExcel2016ActivationCode
ProfessorTeachesExcel2016ActivationCode
ProfessorTeachesExcel2016ActivationCode
ProfessorTeachesExcel2016ActivationCode
ProfessorTeachesExcel2016ActivationCode
ProfessorTeachesExcel2016ActivationCode
ProfessorTeachesExcel2016ActivationCode
ProfessorTeachesExcel2016ActivationCode
ProfessorTeachesExcel2016ActivationCode
ProfessorTeachesExcel2016ActivationCode
ProfessorTeachesExcel2016ActivationCode
ProfessorTeachesExcel2016ActivationCode
ProfessorTeachesExcel2016ActivationCode
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