Anonymous Christian

  • Facebook
  • Google
  • SoundCloud
  • STAY CONNECTED

  • HOME
  • ABOUT US
  • BLOG
  • E-BOOKNEW
    • Other New Christian Books
    • Parable of the 5 Wise and 5 Foolish Virgins by Lord Jesus Christ with Church Fathers in First Christianity and Protestant Reformers Martin Luther & John Wesley
    • Almsgiving and Atonement Mystery – Essays in First Christianity Book
    • Lake of Fire – Hope for the Wicked One Day? – Essays in First Christianity Book
    • First Christianity – Thirty Sixty and Hundredfold Mystery Book
    • Book of 1Enoch – Christ Centered Universalism Mystery – Essays in First Christianity
    • Lost Orthodoxy (Paternal Light – Heart of the Gospel through the Eyes of the Kings of Christian Theology) St. Justin Martyr and St. Irenaeous of Lyons
    • Saviour of The World Book
  • AUDIO
  • LYRICS
  • GALLERY
    • PHOTO
    • VIDEO
  • CONTACT US

OUR BLOG

  • International Mathematical Olympiad IMO 2019 Problem 1

    Anonymous Christian
    Jul 17, 2019
    IMO, MATH, Math Olympiad, Math Olympiad Classes, Math Olympiad Secondary
    Comments Off on International Mathematical Olympiad IMO 2019 Problem 1

    Please find the Questions for Day 1 below (Thank you Mr A for sharing it):

     

     

     

     

     

     

     

    Here’s a frail attempt of mine to try solve Problem 1 to celebrate this remarkable Mathematical Competition.

     

     

     

     

     

     

     

     

     

     

     

     

     

     

     

     

     

     

     

     

     

     

     

     

     

     

     

     

     

     

     

     

     

     

    This argument may probably add rigor:

     

    The fact that ff(x) is defined in definition itself means that the domain of x is the same as the codomain of f(x) proving surjective function for f and the proof is complete.

     

    Why is the domain and codomain equal?

     

    let

     

    f(a) = ff(x)

     

    So,

     

    a = f(x)

     

    Where

     

    a = domain

     

    While

     

    f(x) = Codomain

     

    Thus for each integer a since f(a) is defined by definition, and so is ff(x) , the function may safely be assumed to be surjective, that is for each a exists a f(x).

     

    I do admit this sounds like a pseudo argument based on Convention Writing and that’s why I presented the proof as above.

     

    Here’s another way to say it:

     

    Yes, the last equation

     

    ff(x) = 2 f(x) + c with m = f(x)

     

    Causing

     

    f(m) = 2m + c

     

    Means that

     

    m = domain because what is writable as f(m) causes m = domain by definition.

     

    Hence, f(x) = m = domain due to the possible writing above as a consequence of the given functional equation.

     

    But by definition

     

    f(x) = Codomain

     

    Thus

     

    m = f(x) = domain = codomain

     

    As claimed.

     

    QED

     

     

     

     

     

     

     

     

     

     

     

     

    Regardless whether we are able to solve these Beautiful Mathematical Problems, it does not matter in the Spiritual Context. In this Context, please be particularly careful of the ‘Pride of Life’ which comes as a natural temptation each time we make progress toward such worldly knowledge.

     

     

anonymous-christian

Jonathan Ramachandran is founder at AnonymousChristian.org which serves as a Christian Blog discussing the Greater Hope of Biblical Christian in Christ Alone. He is also an IMO (International Math Coach) and a featuring Guitarist for many bands.

Advertisement

Recent Posts

  • Jonathan Academic and Work CV
  • Book of Doctrine 20 July 2023
  • Chiliasm Book 28 May 2023 Update with Martin Luther First Protestant in Last Chapter
  • Chiliasm Book Latest Update (10 New Chapters Added on 25 April 2023)
  • Did you know – First Christianity Chiliasm Possibility

Search

Advertisement

Categories

  • ages of Ages (22)
  • AIMO (4)
  • AMC (1)
  • APMO (3)
  • Apostolic Fathers (7)
  • ASMO (2)
  • Book of Enoch (8)
  • Calculus (2)
  • Charity (16)
  • ChiliasmBook (5)
  • Christian Leaders (48)
  • DoctrineBook (3)
  • Earning Salvation Fallacy (3)
  • Fatherless and Orphans (13)
  • First Christianity (58)
  • Foreigner (1)
  • Forever (12)
  • Free Choice (18)
  • Gehenna (22)
  • GMC (2)
  • Godliness (2)
  • Gospel Hope for Non Christians (80)
  • Hate and Love (9)
  • Head Covering (5)
  • Heavens Definition in First Christianity (21)
  • Holy Bible Aionion Edition (12)
  • Hundredfold Mystery (4)
  • ICAS (1)
  • IJMO (1)
  • IMC (1)
  • IMO (11)
  • Jewish Hell (12)
  • Justice Human Law (3)
  • KBAT/HOTS (1)
  • KMC (3)
  • Lake of Fire (22)
  • LGBT (2)
  • Marriage (8)
  • Math (174)
  • Math Olympiad (155)
  • Math Olympiad Classes (12)
  • Math Olympiad Primary (11)
  • Math Olympiad Secondary (10)
  • Millennial Reign (9)
  • Money Matters (11)
  • Music (1)
  • MyCV (1)
  • Non Elect Salvation (10)
  • Old Testament (6)
  • OMK (14)
  • Parent Children Duty (2)
  • PMONK (4)
  • Poem (1)
  • Preterism (1)
  • Probability (3)
  • Purgatorial Hell Universalism (35)
  • Puzzle (12)
  • Rapture (3)
  • Reason (1,799)
  • Recapitulation (7)
  • Repentance Afterlife (13)
  • Sabbath and Tithes (5)
  • Sadhu Sundar Singh (3)
  • Saints (6)
  • SASMO (4)
  • Shadow of Death (10)
  • Shepherd of Hermas (13)
  • Sibyline Oracles (9)
  • Singapore Maths (3)
  • Slavery (1)
  • SMOPS (2)
  • Spirit World Visions (9)
  • Statistics (1)
  • Testimony (6)
  • Theology (1,666)
  • Tree of Life (3)
  • Trinity (4)
  • UKMT (1)
  • Uncategorized (7)
  • Unconditional Love (14)
  • Understanding Evil (5)
  • Videos (1)
  • Water of Life (4)
  • Wicked Spirit Saved (15)
  • Women (5)
  • Zionism (6)
© Copyright 2014 - 2023 Anonymous Christian | All Rights Reserved.