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1

Buchanan, O. Lexton. Limits: A transition to calculus. Boston: Houghton Mifflin, 1990.

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2

Schinazi, Rinaldo B. From calculus to analysis. New York: Birkhäuser/Springer, 2012.

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3

Proof theory: Sequent calculi and related formalisms. Boca Raton: CRC Press, Taylor & Francis Group, 2015.

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4

Berardi, Stefano. A sequent calculus for limit computable mathematics (technical report). [Toyonaka-shi]: Sangyō Gijutsu Sōgō Kenkyūjo Shisutemu Kenshō Kenkyū Sentā., 2006.

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5

Bucchianico, Alessandro Di. Probabilistic and analytical aspects of the umbral calculus. [Amsterdam, Netherlands]: Centrum voor Wiskunde en Informatica, 1997.

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6

(Victor), Vinnikov V., ed. Foundations of free noncommutative function theory. Providence, Rhode Island: American Mathematical Society, 2014.

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7

Zaslavski, Alexander J., and Simeon Reich. Infinite products of operators and their applications: A research workshop of the Israel Science Foundation : May 21-24, 2012, Haifa, Israel : Israel mathematical conference proceedings. Providence, Rhode Island: American Mathematical Society, 2015.

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8

Simon, Barry. Basic complex analysis. Providence, Rhode Island: American Mathematical Society, 2015.

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9

Tennant, Neil. Motivating the Rules of Sequent Calculus. Oxford University Press, 2017. http://dx.doi.org/10.1093/oso/9780198777892.003.0005.

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Parallelized elimination rules in natural deduction correspond to Left rules in the sequent calculus; and introduction rules correspond to Right rules. These rules may be construed as inductive clauses in the inductive definition of the notion of sequent proof. There is a natural isomorphism between natural deductions in Core Logic and the sequent proofs that correspond to them. We examine the relations, between sequents, of concentration and dilution; and describe what it is for one sequent to strengthen another. We examine some possible global restrictions on proof-formation, designed to prevent proofs from proving dilutions of sequents already proved by a subproof. We establish the important result that the sequent rules of Core Logic maintain concentration, and we explain its importance for automated proof-search.
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10

Limits; a transition to calculus. Houghton Mifflin, 1985.

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11

Calculus 1: Integrals, theory, techniques, sequences. [Boca Raton, Fla.]: BarCharts, 2004.

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12

Schinazi, Rinaldo B. From Calculus to Analysis. Birkhäuser, 2011.

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13

Lial and Greenwell. Sequences, Series & Other Topics Chapter. Prentice-Hall, 2000.

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14

Mursaleen, M., and S. A. Mohiuddine. Convergence Methods for Double Sequences and Applications. Springer, 2013.

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15

Mursaleen, M., and S. A. Mohiuddine. Convergence Methods for Double Sequences and Applications. Springer, 2016.

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16

Student's Guide to Infinite Series and Sequences. Cambridge University Press, 2018.

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17

Jr, Bernhard W. Bach. A Student's Guide to Infinite Series and Sequences. Cambridge University Press, 2018.

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18

Sequences And Mathematical Induction: In Mathematical Olympiad and Competitions. China: World Scientific Publishing Company Pvt. Ltd., 2019.

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19

Kirillov, A. A., M. L. Gerver, S. I. Gelfand, and N. N. Konstantinov. Sequences, Combinations, Limits (Library of School Mathematics, V. 3). Dover Publications, 2002.

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20

Daugherty, Padric. A decidable sequent calculus theorem prover using controlled contraction. 1988.

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21

Bourchtein, Andrei, and Ludmila Bourchtein. Counterexamples on Uniform Convergence: Sequences, Series, Functions, and Integrals. Wiley & Sons, Incorporated, John, 2017.

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22

Bourchtein, Andrei, and Ludmila Bourchtein. Counterexamples on Uniform Convergence: Sequences, Series, Functions, and Integrals. Wiley & Sons, Incorporated, John, 2017.

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23

Furdui, Ovidiu. Limits, Series, and Fractional Part Integrals: Problems in Mathematical Analysis. Springer, 2013.

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