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Will Quora allow such questions with obvious answers to be asked?I will show you a picture I just took last weekendDo you know where is this place?This is a kitchen in a village primary school just two and half hours driving from Guangzhou, one of top 4 China cities. Don't be fritened, I did not even start telling the stories yet. There are 180 students in this school, most of their parents are out to find some labor job far away from home. The kid will see their parents once a year during Chinese New Year. So you may understand partly why there is such traffic in Chinese New Year. The kids mostly stay with their old grand parents. But they need to actually taking care of themselves and their family. The teacher told us the kids will have spring and autumn leave, sounds good? America also give spring break to students, right? Hold on, for this school, spring and autumn leave is for the kids back to home to help planting and haversting in the field during extremely busy spring and autumn season, imagine those grand parents with those kids in the field vs happy kids in spring break of America.Most of kids will go back to their home during lunch hours and they need to cook for themselves and even for their busy family members. And they are lucky ones, the reason I am showing the photo is that there are 10 to 20 students cooked in this kitchen by themselves, because they lived too far away, around 10km from the school, there is not enough time for them to walk back to home during lunch hours, there is no bus transit between their home to shool and it is mountain road they are walking, every morning they walked to the shool with some rice and vagetables for later cooking their lunch normally without meat.We asked the shool master what do they need, he said books, there is always shortage for the books, and they don't have sports facilities, and they need computers for students, there is only one computer in the school for teachers. Students have no chance to learn computer, the school master is so eagerly to build a computer class so the kids can learn some basic skills so they may have better chance to survive in the future. The reality is most of those kid won't be able to contine study after 14 or latest 15 years old because their family can't support them and need them to go out find a job to support their family. Without additional support those kids can never enter college, what is the chance for them to live a proper life in the future?Yes there are very rich people in China, here is the fancy racing car photo I took the next day after school vist during my dinner in a restaurant. The boss of that restaurant liked to show off his collections, every time I saw different racing cars.So what? When we think back to the children in that school just 2.5 hours driving distance from this fancy car. Will this fancy car be helpful for those children? This is only a very close case, in the vast west and north region there are tens of millions of kids need help.So don't even try to compare America poor people with Chinese poor people. I am just taking normal poor families as sample and didn't touch real homeless people yet. And don't talk about China is the world second largest economy just after America. Those numbers are useless. There are still majority of poor people in China need help, by wealthier Chinese and also by international society.I genuinely hope that some day China's villages will be looked like America's and Chinese farmer will live with dignity just like America's farmer, by then and only by then let's try to answer this question._____________________________________Updates on on Nov 27, 2015To avoid someone may think those kids are studying in caves, just need to add more information about that school.this is the ancestral temple which is hundred year old, 20 years ago, It is the place for student to study before the villagers donated a new school building to accommodate 180 students.This is the main buildingThe classroom, the table and chairs are donated and pretty new.The library, the book shelfs are donated as well, but not much good books for the kids, most of existing books are standard educational materialThe basket ball stand is 20 years old, the wood board sometime will fall down and possibly will hit the kids. but this is their favourite game, maybe the only one before table tennis was donated for them recently.But look at the kid, they are just as smart as cute as any other kids. Their smile is as bright as any other brightest kids in the world. Many of them are studying very hard because study is the only possible way for them to live another kind of live after they grow up.There are something really made me feel so proud for China, But Not the China's GDP is 2nd largest in the world just after America, Not the Olympic game in Beijing, not the Skyscrapers. What makes me feel really proud is there are such huge groups of people reaching their hands back to people who really need help. It made me feel confident some years later, finally China's poor will not be too much behind America's on average.There are two sisters introduced us about this school, they are all Doctors in two major hospitals. They were helping this village for years. Above donations are mainly contributed by them. They told us a lot of stories, one I can remember and it still reoccur to my mind from time to time is as below.A family in this village are in extreme poverty, two brothers with 4 kids in each side, unfortunately in one side the parents are all died 6 or 7 years ago, which mean in another side the parent need to raise 8 kids in the same time without any external support. Those two doctors was helping their kids, they were keeping sending around 100 USD a month so all those kids can keep study. What amazed me the most is that a few elder kids all choose medical school, and the eldest are already a doctor now. I can imagining when those kids saw those two Doctors helping them and encouraging them, every time when they visited the village they will help some elders in the village with all kind of disease, bring medicine to them, cure them. What the influence was taking to those kids, what inspiration was giving to those kid and let them made the wish to choose the career which can help others the most - Doctor.To follow up, The action was taken on Thanks Giving，another Group of people luckily living a better life now were engaged to help those kids very soon.Sep 18, 2017I owe this answer an update. from time to time, I received upvotes for this answer. But I was so neglect to give a proper ending to this answer.It has been almost 2 years. I can still remember the day when I was with those children, I can still remember the lapis sky, the vivid smiling faces. it was right before 2015 Christmas. A Group of volunteers consist of mostly G4 students and their parents went to the School with many donations. During the initial visit, the school principal said they really just need a pair of new basketball stands, and they may need two or three computers for computer class. But the volunteer team also prepared sports ware, backpacks, toy, books, kitchen ware and stationaries. It was such a nice day, the kids from that school and the kids from volunteer team played together, volunteers helped them to paint the classroom walls. Those kids also played friendship basketball match，give and receive gifts etc. It makes people felt so warm when watching those scenes.I didn’t watch most of those scenes, but I had something even nicer. I as a parent with IT background, was entrusted by the kids with computer task. The school principal want two or three computers, I will help them on a computer classroom. With some retired company computers and company IT team’s help. I had 20 sets of working computers came in handy. During the day, those computers were setup in their new COMPUTER CLASSROOM. Then 20+ G4 Kids was invited in the room. I watched them step into the room in awe. This is first computer class in their life. All I can teach them is to power on, login with password, open notepad and type their name.Looked at their smiling faces, their shining eyes, it felt like this is one of best thing in my life. I know it is not enough for them, it is not best computers, they don’t have proper computer desks, but at least, the door is opened and they are getting into the digital era, the world seems not that far aways from them. I am only seeing this in my narrowed eyes. What we did is just so minimum, one time small aids. There are thousands of groups who are helping those underdeveloped regions and their kids continuously.It is not the end of the story. In the mid of 2017, I got to know from school principal that they got a new round of donations. Before those computers aged enough, there is one famous internet company donated a whole new computer room for them. I am so happy to see their students are now all studying in the new environment, new computers, new computer desks, professional cabling, internet access etc.back to the questions itself, in two years. I am still holding the same answer. It won’t be a valid question. Why? because a nation’s true power resided in their poor people instead of the riches. If Chinese poor people are same as American, China will be today’s undoubtedly world’s number one superpower with its 1.3 billion people. It is a simple logic. Imagine China have same minimum wage as America, WOW, how powerful China will be. But it is not the situation today, not now.We Chinese hold the faith that someday, maybe some decades later, China will catch up. Chinese are typically hardworking and smart, looking back into 3500 years of Chinese history. Thanks for so many historians and continues history record in 3500 years. We know as long as there are no wars, as long as government/ruling class don’t do things stupid. Society and economy will thrive.May the peace be with the world.

I have published a detailed comparative etymological analysis on this —can speak German, Dutch, Danish, and Swedish — and my findings basically boil down to: probably yes, but not by nearly the margin that is often assumed. Stated another way: other major Germanic languages, particularly English’s West Germanic cousins German and Dutch, are actually much more Latinized than is often appreciated, and in some domains are actually more Latinized than English is. (For instance the standard German words for “write,” “window,” “bowl,” “stroll,” “body,” “head,” “last” as a verb, “buy,” “sell,” “shave,” “hinge,” “stocks,” “mistake” and many other common everyday terms — all of which are of Germanic origin in English — are of Latin origin in German, more on this below.) If going by sheer proportion of vocabulary, it’s true that the majority of English words are of Latin (or Greco-Latin) origin, but the same is true of German and Dutch too, in part due to the proliferation of Greco-Latin technical terms.The everyday wordstock in all 3 of these languages, including English, is heavily Germanic — think of the lyrics for popular songs, for instance, which tend to be more than 90% Germanic. Yet when it comes to the higher registers of technical, legal, high cultural and other vocabulary, it turns out that German, Dutch, and even most Scandinavian languages — outside of Icelandic — have been thoroughly shaped by Latin lexical borrowings, just like English, both directly and indirectly (through French and other Romance languages). To provide a few examples that may confound our expectations:German, in particular, is full of terms in which standard German generally opts for a Latinate borrowing, while English prefers a Germanic equivalent (either native Anglo-Saxon or borrowed from Old Norse or Dutch). The list below provides a sampling of such cases.German Fenster (window), schreiben (to write), kurz (short), rasieren (to shave), Körper (body), Kopf (head), Scharnier (hinge), Schüssel (bowl), spazieren (to take a walk), kaufen (to buy), verkaufen (to sell), einkaufen (to shop), kämpfen (to fight), sauber (clean), Dusche (shower), Aktien (stocks), both Eimer and Kübel (bucket), fehlen (to be missing), Fehler (mistake), Pleitenserie (losing streak), dauern (to last), Drache (kite), Kummer (sorrow), Panne (mishap), Partie (sports match), Tastatur (keyboard), Taille (waist), Rolle (pulley), Frikadelle (meatball), passieren (happen), Zettel (a sheet, as of paper), Pferd (horse) and many others. (Expanded list here: http://wesulm.angelfire.com/languages/unconventional_wisdom.htm )There are also thousands upon thousands of terms for which German, Dutch, and most Scandinavian languages (the North Germanic group) have borrowed in the same or a highly similar Latin-based loanword. It’s one of the reasons that speakers of one European language are usually able to so rapidly learn another; all of us have borrowed in the same basic technical and standardized Latin-based loanwords. A few instances in German (no translation needed): Diskussion, Allianz, dramatisch, komplett, Komponente, Kategorie, Kommentar, Klasse, Frucht, irritieren, Spirale, Politik, Temperatur, Projekt, Zeremonie, Vehikel, Modell, Literatur, Markt, Pille, sexuell, Sektion, Rolle, romantisch, Papier, Dokument, spezifisch, Natur, nervös, mechanisch, renovieren, reparieren, Nummer, nuklear, Objekt, Preis, Kultur, Leutnant, rund, persönlich, Perspektiv, Priorität, Skrupel, Produkt, Kontrakt, Legende, kompakt, Laboratorium, Kredit, Konflikt, Korridor, Charakter, Appetit, Struktur, enorm, Athlet. A more extensive list here: http://wesulm.angelfire.com/languages/common_grecolatin.htmI call this the “common Greco-Latin” and it can be conceptualized as a common superstratum that unites most Western languages — in a sense, the true common language that underlies the Western world. To clarify, these words were not borrowed into German from English, a common misconception; their cognates were “co-borrowed” independently into both German and English from Latin or Romance languages sources. To further appreciate this, check out the sampling below of words that are spelled exactly the same in English and German and, for the most part, also carry the same meaning. Almost all such terms are of Latin origin — again borrowed independently into the two Germanic languages — instead of Germanic origin. English and German obviously share thousands of such Germanic cognates too, but due to the ancient divergence between the two languages from their common Germanic ancestor, their spelling has likewise diverged in most cases. (Recall that, by convention, nouns in standard German tend to be capitalized.)Addition, Material, Argument, System, Emotion, Episode, absurd, Audio, abrupt, Fort, Origin, Force, Evaluation, Index, Erosion, Manipulation, loyal, Instrument, intelligent, Interpretation, Millennium, sinister, solar, Version, super, Inflammation, journal, Basis, Avenue, Balance, Invasion, Lotion, Agent, Frustration, Graph, Generation, April, September, November, August, normal, Interpretation, Passion, Imitation, Phase, Solution, solid, Transport, transparent, extra, Mission, Mayonnaise, Person, Ovation, Parade, Planet, Plan, Pilot, Position, Portion, Pose, Rose, Navigation.Extended list here: http://wesulm.angelfire.com/languages/kissing_cognates.htmAnd then there’s also a list where English has imported a Latin-based loanword, while German (and often Dutch and the Scandinavian tongues) has simply borrowed in a different choice, but also of Latin (or Greco-Latin) extraction. Examples:German Karte (vs. map), impfen (vs. vaccinate, immunize, or inoculate), Kanal (vs. channel), Büro (vs. office), Datei (vs. computer file), fälschen (vs. counterfeit), kochen (vs. boil), sicher (vs. certain, safe, secure, sure), Schulung (vs. training), Termin (vs appt), Theke (vs. counter), Tinte (vs. ink), Tisch (vs. table), Schreibtisch (vs. desk), spenden (vs. donate), Opfer (vs. sacrifice and victim),Posaune (vs. trombone), Bilanz (vs. record), Fackel (vs. torch), Abonnement (vs. subscription), Schraube (vs. propeller), Fabrik (vs. factory), betonen (vs. emphasize), ausliefern (vs. extradite), Hypothek (vs. mortgage), Imperium (vs. empire), Eigenkapital (vs. equity), Fazit (vs. conclusion), Kerker (vs. dungeon), Krawall (vs. riot), Kreide (vs. chalk), Korb (vs. basket), Apotheke (vs. pharmacy)Extended list here: http://wesulm.angelfire.com/languages/different_latin_loanwords.htmFor further reference here’s my more complete article on this topic (referencing other URL’s): http://wesulm.angelfire.com/languages/english_why_germanic.htmand discussion on ResearchGate:Is English language a Germanic or a Romance language?In conclusion, yes, English likely does have a greater Latinate proportion of its vocabulary than its major West Germanic and North Germanic cousins. It’s also true that German, at least to a point, tends to compound more from its own Germanic stems, using metaphors to generate higher-register vocabulary (though in most cases, German also borrows in the Latin-derived term side-by-side, seehttp://wesulm.angelfire.com/languages/dueling_doublets.htm )But it’s a matter of degree rather than a true qualitative difference. Both German and Dutch, as well as Swedish, Danish, Norwegian, have also been heavily Latinized in their lexicons. They may not have had a singular event like the Norman Conquest to bring this about, but the sheer cultural and intellectual prestige of Latin Europe ultimately had the same basic impact on the vocabularies of almost all the Germanic tongues. (And even then there were some “1066-like events” for the Continental Germanic languages as well, such as French occupation of parts of the Holy Roman Empire in the Thirty Years’ War, Napoleon’s occupation of the Low Countries, and Louis XIV’s expansive power across Europe.)The exception here is Icelandic which is the one true “purist” Germanic language, opting to introduce new vocabulary through loan translation (so-called calques), using roots from its own basic wordstock to create metaphors. This is also what ancient prestige languages, like Mandarin Chinese, tend to do for practical reasons, and it makes even more complex, sophisticated vocabulary more readily apparent to native-speakers in meaning than “borrowers” like English. As kids, we learn the (mostly) Germanic vocabulary first, then have to master an entire layer of (mostly) Latin- and Greek-based “SAT words” as we go through school.But the bottom line is that German, English, Dutch, and most of the Scandinavian languages have the same essential structure. All are heavily Germanic in their core vocabulary — with the overwhelming majority of the Top 100 and Top 1,000 most used words of Germanic extraction, in all cases. Their grammar, syntax, and orthography are also overwhelmingly Germanic, with French, Latin, and Greek having almost no impact on core grammar (though Old Norse, a fellow Germanic language, has helped shape English to drop many cases and inflections). But virtually all Germanic languages save for Icelandic — and including German, English, Dutch, and even Swedish and Danish — have seen their higher registers transformed by a massive influx of Greco-Latin based lexical borrowings and terminology.

This is one noble pursuit, Mikayla, and if you want, and can afford, to start with the basics then my personal advice to you, and to anyone in the similar situation, will be: do it right, do yourself a favor - first learn the basic alphabet or the basic grammar of modern mathematical proofs.Your initial time and effort investment will be comparatively small but you are guaranteed to rip handsome profits later on because the constructs that we briefly highlight below are applicable across all the domains of modern mathematics.Key: get a firm grip on these basic four: NOT, AND, OR, if [math]P[/math] then [math]Q[/math].We explicitly leave the logical values of True and False undefined and we call [math]P[/math] and [math]Q[/math] the sentential variables which can be populated with just about anything we wish. For example, it is perfectly normal to set [math]P[/math] = Lions operate submarines or [math]Q[/math] = Flying walruses waltz on the Moon.NOT is a unary connective - it acts on exactly one argument or operand and it results in negation. The original and the NOTed operands form a contradiction because they have diametrically opposite logical values. In other words, the negated True becomes False while the negated False becomes True.The behavior of multiple consecutive operators NOT mimics that of [math](-1)^n[/math] arithmetic ([math]n\in\mathbb{N}[/math]): a string of an even number of consecutive NOTs does not change the logical value of the subordinate sentence while a string of an odd number of consecutive NOTs is equivalent to applying NOT exactly once. For example, when we tell our kids Do not not do it what we really mean is Make sure that you do it.In the spoken English the operator NOT is applied selectively. When negating the sentenceElephants Can Flywe do not sayNot Elephants Not Can Not FlyWe, rather, utterElephants Can Not FlyIn formal structures, however, the operator NOT plows right through and consumes everything in its path voraciously. For example, [math]P[/math] OR [math]Q[/math] will be negated into (NOT [math]P[/math]) AND (NOT [math]Q[/math]).In some sentences the operator NOT is still applied selectively: the function [math]f(x)=|x|[/math] is NOT differentiable at [math]x=0[/math], the number [math]64[/math] is NOT prime, a distribution is NOT normal and so on.AND (conjunction) is a binary connective - it acts on exactly two operands which are called conjuncts. The logical value of AND evaluates to True in one case only - when the logical values of both of its subordinates are True at the same time. In all the other cases AND evaluates to False.For example, the following constructGreen turtles solve differential equations AND [math]17[/math] is primeevaluates to … False because the logical value of the left operand is clearly False. But this construct([math]\pi>0[/math]) AND ([math]\pi<4[/math])evaluates to True and can be rendered compactly as [math]0<\pi<4[/math].AND is negated as follows: [math]P[/math] AND [math]Q[/math] becomes (NOT [math]P[/math]) OR (NOT [math]Q[/math]).When translated into the formal notation all of the following English words are reincarnated as AND:buthoweverwhilethougheven thoughalthoughneither … nor …For example, the sentenceIt was raining but the sun was outbecomes (It was raining) AND (the sun was out).OR (disjunction) is also a binary connective - it acts on exactly two operands called disjuncts. The logical value of OR evaluates to False in one case only - when the logical values of both of its subordinates are False at the same time. In all the other cases OR evaluates to True.For example, the following constructRoses are red OR Alpha Centauri is [math]4.37[/math] light years away from Earthevaluates to True.While in the spoken English OR sometimes carries the aura of exclusivity, in the formal language OR is always inclusive. For example, giving directions to a lost tourist in Manhattan we can utter on 42-nd and 8-th turn right or go straight (to get to the Central Park Zoo) which implies exclusivity since the tourist (being not a good quantum object) can not be in two distinct places at once.OR is negated as follows: [math]P[/math] OR [math]Q[/math] becomes (NOT [math]P[/math]) AND (NOT [math]Q[/math]).Now that we know what these operators are, what can they do?For starters - they can create!Strung together into a proper shape the atomic stock operators can be used to create (or construct) compound or more complicated ones. For example, here is one, but not the only, way to form an exclusive OR (otherwise known as XOR) operator:([math]P[/math] AND (NOT [math]Q[/math])) OR ((NOT [math]P[/math]) AND [math]Q[/math])IF [math]P[/math] THEN [math]Q[/math] is generally called a conditional - a formation from which the causality can be totally absent. For example, the following is a perfectly legal sample conditional:IF ([math]\pi[/math] is irrational) THEN (binary zebras invented the Bessel functions)The founding fathers of formal logic decided to allow the maximal degree of freedom in that case.In mathematics, however, the causality better always be there. As such, we have the following formula: a conditional + causality = an implication or an inference:IF ([math]a\equiv b \pmod n[/math]) THEN ([math]ac\equiv bc \pmod n[/math])In this particular context, [math]P[/math] is known as a premise, a hypothesis or an antecedent while [math]Q[/math] is known as a consequent or a conclusion.Get used to the following fun fact:the logical value of an inference is False in one case only - when [math]Q[/math], the conclusion, is False and [math]P[/math], the antecedent, is True. In all the other cases an inference evaluates to True, even when the antecedent is False!Intuitively it means that a false premise implies anything - another decision handed down to us by the founding fathers.For example, the following implication:IF (violets are mammals) THEN ([math]\pi > 2[/math])evaluates to True.A conditional is negated as follows: it becomes an AND: [math]P[/math] AND NOT [math]Q[/math]. Example: a sentenceIF (I have $3 in my pocket) THEN (I will buy a loaf of bread)is negated into (even though or despite the fact that) I have $3 in my pocket AND I will not buy a loaf of bread (nonetheless).When translated into the formal notation all of the following English words and phrases are reincarnated as IF [math]P[/math] THEN [math]Q[/math]:[math]P[/math] implies [math]Q[/math]if [math]P[/math] then [math]Q[/math]from [math]P[/math] it follows that [math]Q[/math][math]P[/math] is sufficient for [math]Q[/math]for [math]P[/math] it is necessary that [math]Q[/math][math]P[/math] only if [math]Q[/math]for [math]Q[/math] it is sufficient that [math]P[/math][math]Q[/math] is necessary for [math]P[/math][math]Q[/math] if [math]P[/math][math]Q[/math] whenever [math]P[/math]Closely related to the topic of our discussion are the following four formations or types of a conditional. For the sake of the argument, since we have to key off of something, let us call IF [math]P[/math] THEN [math]Q[/math] a direct statement.Swapping the two predicates in the direct statement results in a converse statement IF [math]Q[/math] THEN [math]P[/math]. Negating the two predicates in the direct statement results in an inverse statement IF NOT [math]P[/math] THEN NOT [math]Q[/math]. Swapping and then negating or negating and then swapping the two predicates in the direct statement results in a contrapositive statement IF NOT [math]Q[/math] THEN NOT [math]P[/math]:*It can be shown that the direct and the contrapositive statements are logically equivalent and so are the inverse and the converse statements. Remember this well.Now that we know what a conditional is, what can it do?*For starters - it can help us prove things!Already?Yep.How so?Say that for demonstration purposes we have the following direct statement in natural numbers [math]n[/math]: if ([math]n^2[/math] is even) then ([math]n[/math] is even) and we have a rough time proving that statement. We rack our brains thisaway and thataway and - nothing goes. Hm. Let us try the contrapositive, maybe we will have a better luck then.As the above contrapositive construction recipe prescribes we may either swap and then negate the predicates or we my negate and then swap them. Let us swap the predicates first to obtainif ([math]n[/math] is even) then ([math]n^2[/math] is even)Then we negate. As discussed earlier, in this case we apply the NOT operator selectively by marrying it to the parity property of the integers:if ([math]n[/math] is NOT even) then ([math]n^2[/math] is NOT even)Lastly, we may give the result a more familiar form ofif ([math]n[/math] is odd) then ([math]n^2[/math] is odd)Now we go to work: if [math]n[/math] is odd then it is representable as [math]n = 2k+1[/math] for some suitable integer [math]k[/math]. Hence, [math]n^2 = 2\left(2k^2+2k\right)+1[/math]. Aha! The object in parenthesis must be a natural number [math]m[/math] because natural numbers are closed under addition and multiplication. Therefore, [math]n^2 = 2m+1[/math], which is odd. What was required to prove.But now observe the magic of conditionals - by the virtue of the logical equivalence we, automatically, proved the direct statement! That is, we actually proved that if ([math]n^2[/math] is even) then ([math]n[/math] is even).We, thus, see that the logical equivalence of conditionals acts as a sort of a bridge which allows us to cover the gaps and connect the arguments that otherwise seem not connectible.I can talk about this for literally hours - there is much more ground to cover here. We, for example, should prove that all are negates to at least one is NOT and conversely. We should prove that at least one is negates to none are and conversely. We should discuss the truth tables construction. We should discuss the infix, the postfix and the prefix notations and so on.The point is - though the surface of formal logic is vast, even the introductory texts run into hundreds of pages, become familiar with the minimum viable material outlined in this answer. A lot can be achieved with just the basic four.The logicians will hopefully supply more modern and/or better choices but you can try these two books to get going:“Introduction to Mathematical Thinking” by Keith Devlin, about 117 pages“Introduction to Logic and to the Methodology of the Deductive Sciences” by Alfred Tarski, about 254 pagesAfter that you can investigate the proofs by contradiction and our favorite (that’s a sarcasm) proofs by induction. Practice. Practice. Practice.Remember:if (talent does not work hard) then (hard work beats talent)Thanks to the monumental effort by Mr. Joyce you can also go to Euclid’s ”Elements” and practice turning its loose statements into their modern equivalents. Yes, Euclid is not rigorous enough. Yes, he missed a lot. But you are after the mechanics. For example, take the statement of B1P5 and make it proper:IF (a planar triangle has a property of being isosceles) THEN (its interior angles at the base are equal one another)Early number theoretic and combinatorial results are also a great - and pretty much infinite - source of practice proofs.If you are familiar with real analysis or complex analysis or graph theory or any other domain of mathematical knowledge, setting the corresponding context, begin the process of realigning or readjusting your attitude and your thought process from being a consumer of some ready-made recipes to becoming a producer of ones.