"Sò͘-ha̍k kui-la̍p-hoat" pán-pún chi-kan bô-kāng--ê tē-hng
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Tē 1 chōa:
'''Sò͘-ha̍k kui-la̍p-hoat''' (mathematical induction) sī 1 chióng [[chèng-bêng]] ê hong-hoat, tiāⁿ ēng lâi chèng-bêng bó͘-mih tîn-su̍t tùi só͘-ū ê [[chū-jiân-sò͘]] (natural number) lóng sī chin--ê. Chit ê hong-hoat ē-tàng khok-chhiong chò [[kiat-kò͘ kui-la̍p-hoat]] (structural induction), ēng tiàm khah it-poaⁿ-te̍k, ū [[liông-ki koan-hē]] (Well-founded relation) ê kiat-kò͘, pí-lūn kóng [[chhiū-á (chi̍p-ha̍p-lūn)]]. [[Sò͘-ha̍k-te̍k ê lô-chek]] ham [[tiān-naú kho-ha̍k]] mā lóng ū leh ēng kiat-kò͘ kui-la̍p-hoat. Sò͘-ha̍k kui-la̍p-hoat ham chiah-ê ū hû-ha̍p [[liông-sū goân-chek]] (well-ordering principle) ê hong-hoat tī [[lô-chek]] téng-koân lóng sio-siâng, in lóng sī [[lô-chek téng-kè]] (logical equivalence) ê hong-hoat.
== Lē ==
Chún kóng lán beh sò͘-ha̍k kui-la̍p-hoat lâi chèng-bêng <math>1 + 2 + 3 + \cdots + n = \frac{n(n + 1)}{2}</math>tùi só͘-ū ê [[chū-jiân-sò͘]] ''n'' lóng sêng-li̍p.
Tē 1 pō͘: ''n'' = 1 ê sî,
:<math>1 = \frac{1(1 + 1)}{2}</math> sêng-li̍p
Tē 2 pō͘: ká-siat ''n'' = ''m'' ê sî sêng-li̍p,
:<math>1 + 2 + \cdots + m = \frac{m(m + 1)}{2}</math>
Tē 3 pō͘: Án-ne ''n'' = ''m + 1'' ê sî,
:<math> 1 + 2 + \cdots + m + (m + 1)
= \frac{m(m + 1)}{2} + (m+ 1)
= \frac{m(m + 1)}{2} + \frac{2(m + 1)}{2}
= \frac{(m + 2)(m + 1)}{2}
= \frac{(m + 1)(m + 2)}{2}
= \frac{(m + 1)((m + 1) + 1)}{2}.
</math>
mā ē sêng-li̍p.
Kin-kì Sò͘-ha̍k kui-la̍p-hoat, <math>1 + 2 + 3 + \cdots + n = \frac{n(n + 1)}{2}</math> tùi só͘-ū ê chū-jiân-sò͘ ''n'' lóng sêng-li̍p. #
{{phí}}
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