FALLACIES 139

The next example of fallacious reasoning involves the
understanding of logarithms.

log(1+x) =x—1x24+1x3 —1xt41x5— | . | etc.

[The logarithms are to the base e.]
If x=1, then log(1 +x) becomes log 2 and

log 2=1—}+3—3+4—4+i—4+ ete.
Multiply this by 2:
2log2=2—1+4+2—-142-142_1 etc.
Collect all terms with common denominator in order of size:

2log2=(2—1)—(3)+(3—-3)—(1) etc.
= 13 — 31+ etc.

which is the same as log 2.

oo |

W

Therefore log 2 =2 log 2
and again I=2

This fallacy is due to the rearrangement of the terms, not all
of the same sign, of an infinite series.

Infinite series also afford another fallacious example.

Let e+ ¢t x
and  HiHEHER AT - - o =
then FEF A E F R U ey
but i 4+ 3 4+ 14 ... o
therefore, subtracting:
$ 4 b 5 =2)—%

but S bk ik 7=y
therefore 2y —xX=y

and Y iy

so that xX—y=0

Now the expression x—jp is equivalent to:
MR A - b

REABBARTTa: Y
BUBHATRE L

i