At Stack Exchange, one's reputation can never decrease below 1. Is negative reputation that is not counted in case of insufficient reputation deducted later on, i.e. when reputation is earned?  EDIT: SOLVED. The point of my question was that it is ambiguous from /other Q&amp;A whether, in the case of insufficient reputation mentioned above, the reputation is not decreased to below 1 just for the time being or the negative reputation is permanently ignored. The doubt was considering the fact that every user's reputation change is recorded, and there are reversions in reputation change in case of deletion of posts.
If a user is the type of person to consecutively get downvoted to potential negative reputation, so be it. What's the reasoning to maintain a minimum of one?  One reason that may justify this is of trying to not deter new users from the site who haven't read the FAQ and unknowingly and wrongly ask or answer a question. But most of us acknowledge this and not downvote in such a scenario.  So what's the reasoning behind this lower bound of 1?
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This fact shows that a one-to-one linear transformation maps a linearly independent set onto a linearly independent set.  All I can think of doing: If $\{T(\mathbf{v}_1), \dots ,T(\mathbf{v}_p)\}$ is linearly dependent, then there exist weights $c_1, \dots, c_p$, not all zero, so that $$c_1 T(\mathbf{v}_1) + \cdots + c_p T(\mathbf{v}_p) = \mathbf{0}$$ Since $T$ is linear: $$c_1 T(\mathbf{v}_1) + \cdots + c_p T(\mathbf{v}_p) = T(c_1\mathbf{v}_1) + \cdots + T(c_p \mathbf{v}_p)=T(c_1 \mathbf{v}_1 +\cdots + c_p \mathbf{v}_p)=\mathbf{0}$$ So the set $\{\mathbf{v}_1, \dots , \mathbf{v}_p \}$ must be linearly dependent. Am I missing something? And why must $T$ be on-to-one for this to be true? An example showing that it is not true if $T$ is not one-to-one would be great! Can fresh pasta sheets be used to assemble a lasagne, then left in the fridge overnight before baking? Or will this make them mushy or otherwise degrade them?  I have recently gotten into making fresh pasta, and I want to prep a lasagne the night before. I have done this before with store-bough dried noodles, but I'm not sure if doing this will have a negative effect on fresh, more delicate pasta. What is the difference between “Size” and “Size on disk?” Looking at the properties for a Windows file I get two attributes, “Size” and “Size on disk,”  and "Size on disk" is always larger.  What do these two metrics mean? "It really doesn't matter" v "It doesn't really matter" I can't distinguish the difference in meaning between these  two sentences.   It really doesn't matter.  It doesn't  really matter.    It seems that there is a nuanced difference, but I cannot see what this is. If $a,b,c$ are positive , show that $$\dfrac{b^2+c^2}{b+c}+\dfrac{c^2+a^2}{c+a}+\dfrac{a^2+b^2}{a+b} \ge a+b+c$$  Trial: Here  I proceed in this way $$\dfrac{b^2+c^2}{b+c}+\dfrac{c^2+a^2}{c+a}+\dfrac{a^2+b^2}{a+b} \ge  \dfrac{2bc}{b+c}+\dfrac{2ca}{c+a}+\dfrac{2ab}{a+b}$$ then how I proceed. Please help. Inexact measurement and wavefunction collapse