In my book the following is written:

When an electron withdrawing atom such as a halogen is attached to the end of a carbon chain, the $\sigma$-electrons of the $\ce{C-X}$ bond are attached to or displaced towards the more electronegative halogen atom, as a result $\ce{X}$ acquires a small negative charge and $\ce{C_1}$ acquires a small positive charge. The small positive charge on the $\ce{C_1}$ in turn attracts the $\sigma$-electrons of the $\ce{C_1-C_2}$ bond towards it. As a result $\ce{C_2}$ acquires a small charge, of course smaller than on $\ce{C_1}$.

Then as $\ce{C_2}$ acquires a small a charge shouldn't the positive charge of $\ce{C_1}$ become less than earlier? Shouldn't it be true?

...This type of a displacement of $\sigma$-electrons along a saturated carbon chain whenever an electron withdrawing group is present the end of the chain is called inductive effect.

Why is there displacement of only $\sigma$-electrons not $\pi$-electrons and why does it happen along a saturated carbon chain only?

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    $\begingroup$ Your, right in 1 case and it seems to me your over interpreting this - it's only an example and inductive effect affects all bonds, but there may be stronger mesomeric effects $\endgroup$ – Mithoron Feb 2 '15 at 13:05

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