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Not really. but there is some confusion in this thread. I see that you are looking for values of x that make the fraction undefined ie division by zero. If x is a real number that is correct. But it is confusing at least and incorrect at worst to say x = 0 works. For the reason you have already given putting x = 0 leads to the fraction being undefined. So x is not equal to 0. We are all agreed on this. You are also correct to note that there is no real number p such that (p2 +1) = 0 So the correct form of reasoning goes that x cannot be equal to p, whatever p might be, since it is not a real number. Thus the only restriction on numbers that you cannot choose for x or must exclude to be x = 0

It is not at odds with what you've read. Bleached coral is not dead. It is just the same living coral but without the symbiotic algae in it. The coral itself is like miniature jelly. It is colorless. The colors are those of the symbiotic algae. The coral without the symbiotic algae is alive for a couple of months. Bleached. Then it starts dying. Corals expel the algae naturally, when the water gets warm, and get the algae back when the water temperature goes down. It is when the water temperature stays warm for too long, which happens recently with the climate change, the bleaching becomes bad for corals. The sunscreen effect, very old news. The signs here remind divers and snorkelers not to use sunscreen - or use special kinds only - for at least 10 years now.

I'm not a mathematician but I think you may be confusing inputs and outputs. As I understand it the domain of a function is the set of inputs it can accept, i.e. the values that x can take. What you seem to be saying is the output, in the case of the function you have chosen, is imaginary rather than a real number.

Nothing at all. I'm sorry, it was me not you. Preparing latex formulae is difficult for me these days as I have to do it on my old computer,save it, and then transfer it to a newer computer when I can get on one. Whilst I was doing this for probably your first of the 'bunch' you must have added more so I only quickly posted in this one which was the wrong thread. Thus I didn't understand why the formula under discussion had 'changed'. I deleted my post but had to put something in its place. Sorry if this caused more confusion. But hey, never mind, I see we have new mathematically minded member so welcome @e jane aran FYI please note the site 5-posts-in- the- first- 24-hours limit. This is a security measure that greatly reduce the rubbish the overworked moderators have to deal with. After that time expires you will be unlimited. Thank you for the help you offered. +1

Thank You all, for taking your time to chime in. @ iNow : That is exactly what I wish to know how. If the present is not satisfying enough, I tend to look into the unpleasant events of the past and attribute those to my current failures. @ Genady : Thank You for the wise words. If I encounter repeated failures in my current endeavors, how do I persist in moving forward without getting lost in past failures? @ Phi for All : Well, I had planned for certain things in the past. All of a sudden, a stranger from nowhere comes and seduces me with words when I was still naive, and drags me into a difficult situation. Just as I was realizing in due course what had happened, the same thing happens through another stranger, again. Had those 2 incidents not happened, my relationship in family and society would have taken a different route. It is as though I have been dragged into an alternate reality ( Back to the Future II ) in completely unexpected situations at completely unexpected times by completely unexpected people. With this background, if I am struggling in the present, those past thoughts join together to make things worse. But if I see some success in the present, I am able to forget those pasts and be hopeful of a better future. My situation is how to be equanimous in the present depending neither on my current successes nor my current failures but on myself alone.

Tl;dr: live in the moment

Only 5 posts allowed on day 1. Fine after. Spammers suck. This protocol helps minimize the annoyance they create.

On what basis have you concluded that the domain is "a complex number", rather than being some portion of the set of real numbers? It should be noted, by the way, that the domain is the set of all values which *are* allowed, not the set of values which are *not* allowed.

My practical suggestion is to realize that these are empty words. You already have left the past if you wanted or not. It is gone and cannot be changed. You move towards the future if you want or not. It is inevitable. Even a dead rock moves towards the future. Forget about slogans and consider the issues at hand.

"If I set the denominator to be 0, the domain will not be found over the real numbers." Does the above-quoted portion mean "If I set the denominator equal to zero, I get no solution; does this mean that the domain is 'all real numbers', because the denominator never makes the rational expression undefined?"? If so, the answer is "yes".

How do you define those terms? Does "leave the past behind" mean never thinking about it anymore? Does it mean forgetting all you've learned from your experiences in the past? Does it mean only thinking about the good parts of the past? I think "move towards the future" assumes there is an ideal future for you if you can figure it out. Am I wrong about that? I think our past shapes and prepares us for what we're doing in the present, and helps us think ahead to prepare for what may happen in the future. Success in the future almost always comes from correctly predicting in the present what you'll need to get or do to achieve it, and that's mostly based on past experience.

A lot of people who find the holocaust horrible today, would have participated at the time. We're all a product of our social environment. I'm 73. When I was young, it would have been unthinkable that homosexual people ( the polite expression at the time ) could marry or adopt, or even hold a public position. You could hear the words "nigger" or "coon" in sitcoms, admittedly spoken by lowlife characters. But to say "fuck" on the air was unthinkable. Now you hear fuck all the time, but the racial slurs are absolutely barred, even in jest. All good stuff, but they are just examples of fundamental culture changes that are all good. But the people haven't changed, it's the culture that's changed. Take people born today, transport them back to the Nazi era, and they would do the same. Nazi Germany grew out of desperate times. People act differently under pressure. They tend to pick on anyone who stands out as different, and blame them for their problems. It's still happening in India, Bangladesh, Burma, China, and not too long ago in Northern Ireland. Those are just examples, not the whole picture. The common factor is human nature, it hasn't gone away, and it's not just Nazis on Jews.

Don't just assert, back it up.

Due to the utter inability of people to back up their own argumentation, I propose a handicap! People can look up ANYTHING on the entire internet to support whatever they say (e.g. random conjectures, junk clickbaits with dodgy support if any at all... anything is better than the zero that I'm seeing), while I am strictly limited to peer-reviewed academic research journals (i.e. not those random non-reviewed / preprint stuff from places like ArXiv) I am being extremely generous. There is simply no excuses now to finally back up what you say, with anything, AT ALL. This is from my search: First paper: Front. Psychol., 05 January 2021 Sec. Cognitive Science Volume 11 - 2020 Artificial Intelligence Is Stupid and Causal Reasoning Will Not Fix It - J. Mark Bishop https://www.frontiersin.org/articles/10.3389/fpsyg.2020.513474/full This is a very solid argument, starting at section 6, where he goes into Searle's CRA in a more detailed and nuanced way than I had. The comparison between the understanding of English and non-understanding of Chinese by the same person in the face of functional "as-if" (non)understanding is well-explained here. Section 7 goes into how Godelian arguments further disproves computationalism. It demonstrates how mental procedures aren't containable in formal systems. What's cognitive isn't computational, which is the position of Penrose. Section 8 basically says this: If you subscribe to the idea that machines can possess phenomenal consciousness, then you MUST also subscribe to a form of pansychism. If you do that, you abandon any and all positions on "emergent" consciousness from anything (no great loss since it's false anyway...) Second paper: Consciousness and Cognition, Volume 45, October 2016, Pages 210-225 Artificial consciousness and the consciousness-attention dissociation - H.H. Halajian, C Montemayor https://www.sciencedirect.com/science/article/pii/S1053810016301817 This paper, full of references to scientific research, demonstrating the impossibility of implementation of emotional "routines" that aren't mere simulations. This is taking a different approach than the a priori methods of the other paper, looking at biological and evolutionary mechanisms. Before anyone says "who cares about emotions" here is a quote from the intro portion of the paper (emphasis mine): Well, that's it for now. Take at it, people! p.s. you also need to state what the source(s) you're pointing to is/are talking about, and not just a random link dump.

Wasn’t me, but rather likely related to calling Hitler a gentle soul in comparison to the modern ultra right Israeli leadership. That’s hyperbolic in the extreme and suggests a deep lack of moderation and measure in one’s tone…even though the current cabal under Bibi is hardly acting in ways I can support.

I really expect at least one item from someone, anyone, after half a year, that backs up what they say in any way whatsoever. All anyone had to do, was look up Wikipedia, to find that one reference to Chalmers' Computational Foundation argument. I'd say that Wikipedia's even a bit slanted in this regard, listing Chalmer's "pro artificial consciousness point" and... nobody else's anything. However, Chalmer's position ends up being nothing else than another variety of functionalism. Those random Wikipedia editors are pretty disappointing too. In other developments: Robert Marks, Distinguished Professor of Electrical & Computer Engineering at Baylor and director of The Walter Bradley Center for Natural & Artificial Intelligence, read my article, deemed it to be very good and recommended me to submit it for reprint at the center's online publication. It has now been reprinted there in three parts: Artificial Consciousness Remains Impossible (Part 1) Artificial Consciousness Remains Impossible (Part 2) Artificial Consciousness Remains Impossible (Part 3) Coincidentally, a few months after I originally wrote the article, the UN agency UNESCO banned AI legal personhood in their AI ethics recommendations, adopted by all 193 member states at the time. I wrote to Gabriela Ramos, Assistant Director-General for Social and Human Sciences of UNESCO. She agreed to forward my argumentation to members of her organization in support and defense of the policy. In my view, not only would be AI legal personhood be unethical, it would be flat out immoral (see section "Some implications with the impossibility of artificial consciousness" of my article). There already have been legal arguments made questioning AI legal personhood, one of which is this one: https://www.cambridge.org/core/journals/international-and-comparative-law-quarterly/article/artificial-intelligence-and-the-limits-of-legal-personality/1859C6E12F75046309C60C150AB31A29 There is still a lack of multilateral public discussion and debate. A newspaper article's writer agreed to talk to his editor to see if it's possible to set up a written philosophical debate with me and some field experts named in an article. The usual responses I get from these things are that people don't have the time, but that won't stop me from trying. There are many people from AI-related fields that have expressed similar frustrations on how the current wave of hype is distorting perception of various issues. Edit: See item 68 (text bolded by me): https://unesdoc.unesco.org/ark:/48223/pf0000381137