This is from the book by D.J. Velleman-"How to prove it?" Sec 3.5 Excercise 31:  Prove $\exists x(P(x)\rightarrow\forall y P(y))$  Suppose the universe of discourse is set of all men.   Let statement P(x) $:=$ $x$ is married. Then $\forall yP(y)$ means all men are married. Thus, there exists a man, if his marital status is married that means are all men are married. Am I interpreting the statement correctly? It is not abvious to me why this statement is true at all.
Why is this true?  $(\exists x)(P(x) \Rightarrow (\forall y) P(y))$
What measures does Cognito Forms take to ensure Privacy/ Security Level for Completed Forms/ User Data? Some forms may contain confidential information - even something basic like where a person lives.   What measures do Cognito Forms take to ensure that data stored within its site is secure? Execute shell script or command on idle time I'm searching for the possibility to execute a shell script or command based on idle time in the bash shell.  As an example, if I'm in a SSH session to a server of mine and after X minutes of inactivity in the terminal, I want a command to start a desired program like cmatrix, and when I come back and press a key I will get back where I left. Why does the image not appear? In which US accent is “again” pronounced /əˈɡeɪn/ with the FACE vowel, not /əˈɡɛn/ with the DRESS vowel? Most dictionaries provide the US pronunciation of “again” as /əˈɡɛn/ (uh-gen) with the DRESS vowel. This is the most common pronunciation in the USA. However, I think I might have also come across /əˈɡeɪn/ (uh-gain) with the FACE vowel. This sounds like the word “gain” with an “a” at the beginning. Is there a US accent where “again” is pronounced this way? Best way to track onchange as-you-type in input type="text"? How can I merge properties of two JavaScript objects dynamically? I need to be able to merge two (very simple) JavaScript objects at runtime.  For example I'd like to:  var obj1 = { food: 'pizza', car: 'ford' } var obj2 = { animal: 'dog' }  obj1.merge(obj2);  //obj1 now has three properties: food, car, and animal   Does anyone have a script for this or know of a built in way to do this?  I do not need recursion, and I do not need to merge functions, just methods on flat objects. Why can't a single ReLU learn a ReLU? As a follow-up to  I simplified even more and tried to train a single ReLU (with random weight) to a single ReLU.  This is the simplest network there is, and yet half the time it fails to converge.  If the initial guess is in the same orientation as the target, it learns quickly and converges to the correct weight of 1:      If the initial guess is "backwards", it gets stuck at a weight of zero and never goes through it to the region of lower loss:        I don't understand why.  Shouldn't gradient descent easily follow the loss curve to the global minima?  Example code:  from tensorflow.keras.models import Sequential from tensorflow.keras.layers import Dense, ReLU from tensorflow import keras import numpy as np import matplotlib.pyplot as plt  batch = 1000   def tests():     while True:         test = np.random.randn(batch)          # Generate ReLU test case         X = test         Y = test.copy()         Y[Y &lt; 0] = 0          yield X, Y   model = Sequential([Dense(1, input_dim=1, activation=None, use_bias=False)]) model.add(ReLU()) model.set_weights([[[-10]]])  model.compile(loss='mean_squared_error', optimizer='sgd')   class LossHistory(keras.callbacks.Callback):     def on_train_begin(self, logs={}):         self.losses = []         self.weights = []         self.n = 0         self.n += 1      def on_epoch_end(self, batch, logs={}):         self.losses.append(logs.get('loss'))         w = model.get_weights()         self.weights.append([x.flatten()[0] for x in w])         self.n += 1   history = LossHistory()  model.fit_generator(tests(), steps_per_epoch=100, epochs=20,                     callbacks=[history])  fig, (ax1, ax2) = plt.subplots(2, 1, True, num='Learning')  ax1.set_title('ReLU learning ReLU') ax1.semilogy(history.losses) ax1.set_ylabel('Loss') ax1.grid(True, which="both") ax1.margins(0, 0.05)  ax2.plot(history.weights) ax2.set_ylabel('Weight') ax2.set_xlabel('Epoch') ax2.grid(True, which="both") ax2.margins(0, 0.05)  plt.tight_layout() plt.show()     Similar things happen if I add bias: 2D loss function is smooth and simple, but if the relu starts upside down, it circles around and gets stuck (red starting points), and doesn't follow the gradient down to the minimum (like it does for blue starting points):    Similar things happen if I add output weight and bias, too.  (It will flip left-to-right, or down-to-up, but not both.) This is similar to , except it's a bug report, not a feature request.  Currently, the nominee's comments on his/her own post are not highlights, unless you click "add / show more comments"  When the page is loaded it looks like:    AfterI click "add / show more comments", it becomes:    Could we have the blue highlighting on the post owner's comments there all the time? It becomes difficult to see the nominees responses to questions, especially on nominations where there aren't enough comments to enable the "add / show more comments" features, like Matt's. Unable to cover get set in apex test class I am unable to cover the following class get set method. Need help in creating test class  public class Aresult{      public class Parent {         public String type {get; set;}         public String id {get; set;}         public String sequence_id {get; set;}         public String etag {get; set;}         public String name {get; set;}     } }   Please suggest  @isTest  public class CirriusGetItemsResultTest {     public static void myUnitTest(){         Aresult.parent a = new Aresult.parent();         a.type='hello';         a.id='hello';         a.sequence_id ='hello';         a.etag ='hello';         a.name ='hello';     } } Why don't applications update by calculating difference? Windows 10 upgrade assistant stuck at 99% Installed Windows 7 Ultimate (64-bit) on a fresh PC and after installing service pack 1 started the upgrade to Windows 10. The assistant app downloads and verifies but gets stuck at 99% in the upgrading window phase. Even after hours it remains stuck there.  I've tried to reboot the machine and that doesn't help either. I've googled and found out that others have faced the exact problem but so far there isn't any solution that works.  Has anyone seen that situation and is there a fix for it? I am a little bit confused about the Area Under Curve (AUC) of ROC and the overall accuracy.  Will the AUC be proportional to the overall accuracy? In other words, when we have a larger overall accuracy will we definitely a get larger AUC? Or are they by definition positively correlated?  If they are positively correlated, why do we bother reporting both of them in some publications?  In real case, I performed some classification task and got the results as follows: classifier A got an accuracy 85% and AUC of 0.98 and classifier B got an accuracy of 93% and AUC of 0.92. Question is, which classifier is better? Is it possible to get results similar to these (or do my results indicate a bug in my implementation)? Creating an arbitrary state of the quantum simple harmonic oscillator How to pass parameters to query? I'm granted a one-entry Schengen visa and now I can't go. Will having an unused visa in my travel passport have any consequences like future visas refusal? Do I need to do anything special? PHP function substr() error Changing console font on Ubuntu 10.04 Server How can I change local console font on Ubuntu 10.04 Server to Inconsolata? Sequences in $C(X)$ converging uniformly implies uniform boundedness and equicontinuity Let $X$ be a metric space and let $\{ f_n \}_{n \geq 1}$ be a sequence in $C(X)$. Show that if $\{ f_n \}_{n \geq 1}$ converges uniformly on $X$ then $\{ f_n \}_{n \geq 1}$ is both uniformly bounded and equicontinuous.  Could I get a hint? On Cesàro convergence: If $ x_n \to x $ then $ z_n = \frac{x_1 + \dots +x_n}{n} \to x $ I am currently undergoing a full Apostol Calculus I reading, and with few chapters left I've began planning what other books to read. I was thinking about finishing both Apostol Calculus l and ll, and then read Apostol mathematical analysis. I'm not pretty sure whether these are the best books or if they will provide me with a strong math basis. I've already taken calculus i, ii, iii and linear algebra. The reason I've chosen Aapostol volume 1 and 2 is that I've heard they cover almost all the topics I've seen and will see in the next semester/s. I would appreciate if somebody could give me some advice about this. I really like to have a book that really gives me hard and challenging problems. I don't know whether to read Spivak Calculus book or not.