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Is there a sequence of non-zero bounded smooth functions $f_1,f_2,\ldots,f_k$ so that
$$\sum_{I=1}^k \cos(f_i)= \cos\left(\sum_{i=1}^k f_i \right)$$$$\sum_{I=1}^k \cos(f_i)= \cos\left(\sum_{i=1}^k f_i \right).$$
andAnd what about the infinite case ?
$$\sum_{I=1}^k \cos(f_i)= \cos\left(\sum_{i=1}^k f_i \right)$$
and what about the infinite case ?
$$\sum_{I=1}^k \cos(f_i)= \cos\left(\sum_{i=1}^k f_i \right).$$
And what about the infinite case ?
Is there a sequence of non zero-zero bounded smooth functions $f_1,f_2,...f_k$$f_1,f_2,\ldots,f_k$ so that
$$\sum_{I=1}^{k}{\cos(f_i)}= \cos(\sum_{i=1}^{k}{f_i})$$$$\sum_{I=1}^k \cos(f_i)= \cos\left(\sum_{i=1}^k f_i \right)$$
Is there a sequence of non zero bounded smooth functions $f_1,f_2,...f_k$ so that
$$\sum_{I=1}^{k}{\cos(f_i)}= \cos(\sum_{i=1}^{k}{f_i})$$
