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abstract algebra - Prove that 1+1=2 - Mathematics Stack Exchange Possible Duplicate: How do I convince someone that 1 + 1 = 2 1 + 1 = 2 may not necessarily be true? I once read that some mathematicians provided a very length proof of 1 + 1 = 2 1 + 1 = 2 Can you think of some way to extend mathematical rigor to present a long proof of that equation? I'm not asking for a proof, but rather for some outline what one would consider to make the derivation as
What would happen if suddenly, 1+1=2 is disproved? 1+1=2 is a necessary truth---roughly, a statement that is true in every possible world Your question, thus, is asking for true counterfactual conditionals with impossible antecedents
Formula for $1^2+2^2+3^2+. . . +n^2$ - Mathematics Stack Exchange (n + 1)3 −n3 = 3n2 + 3n + 1 (n + 1) 3 n 3 = 3 n 2 + 3 n + 1 - so it is clear that the n2 n 2 terms can be added (with some lower-order terms attached) by adding the differences of cubes, giving a leading term in n3 n 3 The factor 1 3 attached to the n3 n 3 term is also obvious from this observation You can use induction to show that the lower-order terms can be dealt with using lower order
Prove that $1^3 + 2^3 + . . . + n^3 = (1+ 2 + . . . + n)^2$ Do you know a simpler expression for 1 + 2 + … + k 1 + 2 + + k? (Once you get the computational details worked out, you can arrange them more neatly than this; I wrote this specifically to suggest a way to proceed from where you got stuck )
Proof that $1+2+3+4+\\cdots+n = \\frac{n\\times(n+1)}2$ Why is $1+2+3+4+\ldots+n = \dfrac {n\times (n+1)}2$ $\space$ ?Not appropriate for an answer, but you've asked either a very easy or a very difficult question If by "why" you mean, "Can I see a proof of this fact?" the question is fairly easy to answer If by "why" you mean, "Why should this be true?" you've asked a very deep kind of question that mathematicians make entire careers out of